Complex Systems Must Be Solved with Systematic Solution; How can We Solve Systematic Problem Such as Ecosystems Using Systematic Solution Dynamically

Complex Systems Must Be Solved with Systematic Solution; How can We Solve Systematic Problem Such as Ecosystems Using Systematic Solution Dynamically | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Complex Systems Must Be Solved with Systematic Solution; How can We Solve Systematic Problem Such as Ecosystems Using Systematic Solution Dynamically Deok soo Cha, kyoun il Kim This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6101727/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study presents a complete solution using a different method from the chaos theory currently used to solve complex systems; therefore, the reader must decide whether to choose it. Over the past 300 years, complex systems with non-quantitative and non-qualitative characteristics, such as ecosystems, have been solved using the chaos theory of statistical physics based on vertical (logical) thinking. However, the new solution is completely new because it is dynamically solved. In other words, unlike the existing one, the new solution views the complex system as a systematic problem that fluctuates endlessly over time and solves it in real time using a systematic solution based on systems thinking with the theory of system analysis that emerged in the 20th century. To solve this problem, we used a method of modeling the ecosystem as a basic model system and reproduced it in real time using a computer and simulator. Therefore, this is different from the chaos theory, which is static and solved in a stationary state. Fortunately, the new solution does not overlap or conflict with the existing logical solution (chaos theory); therefore, we will have to use both solutions. dynamic systems systems thinking chaos theory nonlinear dynamics Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Article Highlight • This study succeeded in solving complex systems that exhibit nonlinear dynamics and complexity by using a new systematic solution based on systems thinking. • It is a new systematic solution that does not overlap and contradicts the logical solution (chaos theory). Therefore, we should adopt both logical and systematic solutions. • It can be proved and simulated in real time through [modeling + simulation] using MATLAB or a simulator 1. Introduction This paper aims to find and publish a solution to the complex system that has not been solved yet. The method has been treated as a static problem for a long time, but in this paper, unlike that, it is considered as a dynamic problem that changes over time and is solved in real time using a recently appeared systematic solution. In other words, this study presents a dynamic solution for complex systems that exhibit nonlinear dynamics and complexity [ 1 ] in nature, such as ecosystems and economic systems. Then, this research result will be provided to systems scientists and other scientists, including deterministic physicists. Before beginning, this study presents two suggestions for readers. First, I hope that readers decide whether to adopt the results of this study. If readers think that the new solution here is reasonable, I hope that they will choose it without hesitation. If not, I hope that they will continue to use the chaos theory of statistical physics, which has been used for the past 300 years. There are no problems and no one will be harmed. Next, this study cites the theory of system analysis in the control theory as a mathematical tool. Physicists need prior knowledge of this issue. [Note: This mathematical tool was created by engineers in the 20th century, but was not used because traditional physics contradicts determinism.] Here is a special comment. This paper asked various questions to the AI ​​system and received them, but the ones that were specifically mentioned here were marked. In the 20th century, complex systems were one of the most difficult problems in science. [Black holes/solar magnetism/superconductivity/nuclear theory/nuclear fusion/plasma/turbulence/climate change/complex systems/consciousness] It includes seven millennium mathematical problems that scientists are trying to solve. We will try to solve the ninth complex system among the ten that are difficult for anyone to solve. The method is to investigate the reason why complex systems are not solved and to solve them by utilizing the dynamic system characteristics of complex systems such as ecosystems or stock markets that fluctuate over time. This method has not been reported previously. To succeed in solving this problem, we must first understand why scientists have not been able to solve complex systems for 300 years. As a result of the investigation, the following conclusions were reached. Although both physicists and non-physicists (especially systems scientists) study complex systems as their research goals, they approach them using different academic methods. In addition, physicists approach the nonlinearity and complexity exhibited by complex systems based on determinism as an object (black box), but ignore the dynamic characteristics and self-regulating functions hidden in the system. This is why physicists have not been able to solve these problems. [Note; They have already rejected to adopt it, claiming that the solution is beyond the scope of physics and mathematics. ('23.11. 04, '24.04. 04) Then, physicists should not approach this research.] Next, systems scientists state that complex systems are not free from determinism. They see the self-regulating function as difficult to handle in a dynamic way. Instead, they build a precise simulator of all dynamic systems and reproduce them repeatedly to solve the complex system by [modeling and simulation]. A representative case is the system dynamics. [Note: This is a useful solution, but it is imperfect. Consequently, no one has been able to solve complex problems for 300 years]. However, we did not need to worry about this. We can solve this problem without a static solution that is considered to be stationary, but with a dynamic solution that changes over time. However, this solution cannot be found in deterministic physics. It is a solution that can simultaneously see both forests and trees at the same time. The solution is presented in Section 2 . [Remark; The 'Note' inserted in this paper is inserted for the reviewer. It will be removed.] 2. Martials and Methods 2.1. Scientific Background This section presents a method to consider complex systems as closed-loop systems and solve them dynamically. If readers approach complex systems as objects like deterministic physicists and view them as static problems, they will have difficulty understanding this solution. In that case, they can use existing chaos theory and there will be no problem. I hope there is no misunderstanding. However, if readers are systems scientists, they will have no difficulty understanding this solution. For example, this is like an internist appearing in the Middle Ages when there were only surgeons or the appearance of an electric car in a world where there were only engine cars. This is the ideal relationship. In the future, we should follow (logical solution + systematic solution): [ 3 ] [Note; If physicists and mathematicians have been misunderstood as replacing their existing solutions with a new systematic solution, other scientists have no reason to receive their consent. However, it has nothing to do with other scientists]. Preliminary Knowledge; Here: For scientists other than system scientists, it is necessary to explain what a systematic solution is. [Note: Please check here what the difference between a ‘systemic’ solution (analyzing the entire system and find a basic solution.) and a 'systematic solution' is; Chat GPT] This can be explained with Fig. 1 (a–b). A system scientist including other scientists understand that the ecosystem (stock market) in Fig. 1 (a) can be replaced by a dynamic system consisting of four elements: input U(s), process Q(s), feedback H(s), and output Y(s), as shown in Fig. 1 (b). [Note: This is also consistent with the internal structure of AI systems]. In particular, if feedback H(s) in Fig. 1 (b) does not exist, it is an open-loop system. This is an algebraic problem and is not called a system. In other case, if H(s) exists, the system is a self-regulating system, such as an ecosystem. In this case, there are active and passive elements inside, and the sum of the two elements continuously converges to zero (energy conservation) The basic model system is shown in Fig. 1 (b). Historical background: According to the literature review results [ 4 ][ 5 ], there has been no case of defining and dynamically solving complex systems as systematic problems based on systems thinking for the past 300 years. A more obvious reason is that physicists have treated them as black boxes based on determinism. [Note: Determinism in physics has not treated non-reversible, non-measurable, and non-reproducible problems.] On the other hand, systems scientists have understood that complex systems are closed-loop systems owing to the influence of determinism, but have not been able to convert and solve them as closed-loop systems with self-regulating functions, as shown in Fig. 1 (b). This paper presents the methods in this study. Fortunately, however, systems analysis theory appeared in the 20th century, so any scientist who understood it can solve it. Consequently, in 2024, a third-party scientist succeeded in solving the complex system dynamically in real time. If we can successfully solve this complex system, what can we gain from it? The results are also non-quantitative and non-qualitative, but they can help us understand the source of the complexity and predict the trends. However, this research was completed by a non-physicist and not a physicist. Likewise, there are cases where non-physicists, not physicists, have studied complex systems. A representative example is the Ilya Prigogine, a Nobel Prize winner. He is an expert in complexity. About 30 years ago, in 1997, he presented a very important conclusion in 'The End of Certainty' [ 6 ]: [Determinism must coexist with indeterminism], and Nobel Prize winner Murray Gell-Mann also agreed with this assertion. However, most physicists and mathematicians ignore his prediction, but other scientists will prove his assertion in 2025, and we should pay tribute to him. Complex systems are characterized by systematic problems. [Chat GPT] If so, then most systems scientists except determinists can understand this, because they dynamically approach the system. If we understand this, we first need to understand the internal structure of a system with self-regulating capabilities, such as a food chain in an ecosystem. According to the literature, a system is defined as "a set of interacting or interrelated elements that operate according to a set of rules to form an integrated whole." However, it is missing self-regulating functions is determinism. Therefore, if we assume a system to be a time-series function, we can solve this very easily. For example, autonomous speed control of a steam locomotive is the application of a self-regulating system. It maintains a constant speed using a device (governor) that combines an element that tries to increase speed and a feedback element that is inversely proportional to the speed. (See the Appendix .) This is explained by the [demand and supply curve] [ 7 ] in economics, as shown in Fig. 2(c). If the two entropy curves (supply and demand) both increase, the two curves intersect. In this case, because the two elements have a time difference d, the intersection point will move left and right endlessly. As a result, the market price will move endlessly over time to converge to equilibrium and eventually converge to a constant price [ 8 ] [ 9 ]; [Note: Adam Smith's invisible hand. This is why the huge and complex natural world maintains equilibrium (stability).] In this case, it is modeled as a feedback system, as shown in Fig. 1 (b), and solved using system analysis theory, as shown in Fig. 2(a) [ 10 ] [ 11 ]. However, many scientists are concerned about how to model large, complex, and difficult-to-solve economic and social phenomena as a basic model system, as shown in Fig. 1 (b). [Note; The system analysis theory suggests a method to simplify and model even the most complex system as a single basic system, so there is no need to be appropriate at all.] Moreover, there is no difficulty because the analysis process can be performed using a computer or simulator. To improve our understanding, we applied the self-regulating function mentioned above to the ecosystem. As mentioned above, it can be divided into active and passive elements in the food chain, such as predator q(t) and prey h(t). The two elements are in the same space; therefore, both increasing curves intersect each other, such as the demand and supply curves in Fig. 2(c). However, there was a delay between the two. [Note: This requires the growth time of organisms in an ecosystem.] In this case, the following equation must be satisfied: $$\:d/dt\left\{q\right(t)+h(t-d\left)\right\}=0\:$$ [Note; This equation is used to find the case where the sum of the number of predators q(t) and the number of prey h(t) is minimum (zero); this is because the system tries to maintain equilibrium. Then, we can model it as a system with the same mechanism as the feedback system. This is the highlight. [Note; If anyone cannot understand the meaning of the above equation, they cannot solve the systematic solution.] As a result, we can model the ecosystem as a basic system, as shown in Fig. 2(d). This paper will then reproduce the complexity that actually appears in the ecosystem based on the explanation so far. Note that physicists and mathematicians cannot criticize this because it is something that systems scientists should solve. Determinists who regarded the system as a black box were excluded. 2.3. Process of Modeling and Simulations 2.3.1. Modeling This study explains why scientists have not been able to solve complex systems in a new manner. As a result, if someone succeeds in modeling a complex system such as an ecosystem, as shown in Fig. 2(d), they can reproduce the complexity and nonlinearity through experiments. [ 12 ] of the size of the ecosystem, stock market, or social phenomena, it can be transformed into a basic system, as shown in Fig. 2(d). [Note: For this method, refer to the control theory textbook.] The transfer function (parameter) of the model system is expressed as equations ( 1 ) and (2) below: This is described using the Laplace operator [ 13 ], which replaces the complex differential equation. [Note; For the reason for using the Laplace transform here and the specific method, refer to the textbook or Chat GPT.]; Specifically, [s] represents the Laplace operator for solving the time-series function, β represents the damping coefficient of the system, and ω represents the natural frequency. $$\:\begin{array}{c}\:\:\\\:\:\:output\:Y\left(s\right)=parameter\:F\left(s\right)\bullet\:input\:U\left(s\right)\:\:\:\:\end{array}$$ 1 \(\:F\left(s\right)=\frac{Y\left(s\right)}{U\left(s\right)}=\frac{G\left(s\right)}{1+G\left(s\right)H\left(s\right)}=\frac{{\omega\:}^{2}}{{s}^{2}+2\beta\:\omega\:s+{\omega\:}^{2}}\) → example ( \(\:\frac{1}{\:{s}^{2}+0.4s+1}\:)\) \(\:\beta\:=0.2\) (2) (Commentary) If you are a system scientist, Eq. (2) is the parameter (transfer function) of all dynamic systems existing in nature. Solving this problem manually is extremely complex and difficult. In this case, the output of the complex system can be reproduced, as shown in Fig. 3 (b), using the commercial program MATLAB [ 14 ], as shown in Fig. 3 (a). (the virtual transfer function at this time is \(\:F\left(s\right)=1/(s^2+0.4s+1)\) ) Finally, by applying the above two equations to solve the output of the model system in Fig. 2(d) though the Laplace reverse transform, we obtained the result in Eq. (3), which represents the response generated when a basic function [Note: unit step function is defined as: if t=0, u(t)=0; if t>0, u(t)=1) is applied. The output of the dynamic systems is highlighted in this study. $$\:{Y\left(s\right)}^{-1}=y\left(t\right)=1-A\bullet\:{e}^{-B\:\bullet\:\:t}{sin}\begin{array}{c}\:\:\\\:\:\left(W\:\bullet\:\:t\:+\:\phi\:\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(3\right)\end{array}$$ $$\:{where},\begin{array}{c}\:\:\\\:\:\:\left[\:A=\frac{1}{\sqrt{1-{\beta\:}^{2}}},\:\:\:B=\beta\:\omega\:,\:\:W=\omega\:\sqrt{1-{\beta\:}^{2}\:},\:\:\phi\:={{cos}}^{-1}\beta\:\:\right]\end{array}$$ If you are a systems scientist or a scientist who understands control theory, you will understand that Eq. (3) is the fundamental response that all systems exhibit. This overlaps exponential and periodic functions. Therefore, it implements periodicity, self-organization, and initial phenomena, and if a random function is input, irregularity is added to the output, thereby exhibiting typical complexity. Please refer to Figs. 3 (a) and 3(b). ULR https://www.youtube.com/watch?v=DrfyX9o3x7A&feature=youtube . 2.3.2. Experiment - Computer and Analog Simulator This paper introduces a method to reproduce the complex system in the above section on a computer, and presents the results in Fig. 3 (b). It can be observed that the input and output are irreversible. Because anyone can reproduce this using the MATLB program, I recommend that you try it yourself. However, there is an analog simulator that is more realistic than the computer simulation above, and reproduces accurate results in real time [Note: The internal structure of the simulator is shown in Figure. 5(a)]. We can confirm The response to the basic function was confirmed, as shown in Figure. 4(b), and the response to the random function, as shown in Figure. 4(c). Paradoxically, this figure shows that complex systems are systematic problems. (Verification) By randomly changing the inputs of the above model system and observing the output over a long period of time, we can discover the complexity in its output; unique characteristics of complex system outputs, such as irregularity, regularity, self-organization, and initial phenomena, can be observed. A video clip has been provided to illustrate this process [ 15 ]. Through this approach, we reproduce nonlinear dynamics and complexity, demonstrating that these are not algebraic (logical) issues , but systematic challenges. 2.4. Application Examples To prove the new solution, this study presents three application cases, which illustrate a comparison between existing algebraic solutions and the proposed systematic solutions. 2.4.1 Re-definitions of Logistic Curve in Ecology (Background): The first is the logistic curve in common sense [Note: This is a famous theory; therefore, only the results are presented. [ 16 ] This is the logistic curve, and the function is defined as \(\:F\left(s\right)=\frac{1}{{1+e}^{-x}\:}\) . It is expressed as a finite function in the static state. As is already known, Verhulst intuitively recognized that population growth and decline are periodic, and based on this, devised a sigmoid function and curve [S]. (Modeling and simulation): However, this is not an ideal solution because it is not a static problem; we solved it as a dynamic problem in real-time. For example, can be determined using Eq. (3), which shows the output of the ecosystem model. If the damping factor of the equation has no damping (β = 0), then the output of Eq. (3) is determined as a periodic function y(t) = 1 – sin (ωt). This is a periodic function with a frequency ω. If this is represented as a dimensionless graph, we obtain a sigmoid [S] curve. (Verification) Given that the population growth of an ecosystem is a dynamic problem, it must be solved in real-time. Thus, it initially grows exponentially, then gradually saturates, and exhibits a sine curve that repeatedly increases or decreases along the curve. 2.4.2. Redefinitions of Lorenz’s Butterfly Effect (Background) A representative example is Lorenz's butterfly effect [ 17 ], which is part of the chaos theory created by statistical physicists. This claim was first made in 1963, just 80 years ago, and has remained unchanged since then. However, this can be resolved using Eq. (3), as presented above. (Modeling and simulation): Model the ecosystem (stock market) as a model system, as shown in Fig. 2(d), and assume that its output function is as shown in Eq. (3). In this case, if the damping factor β included in the transfer function of the model system is underdamped, the initial output of the model system overshoots, as shown in Fig. 5 (b), similar to a lightning surge. However, there is no problem because the overshoot increases rapidly, but disappears momentarily and returns to the original state. This is a unique property of all the dynamic systems. (Verification): This experimental result differs from that of Lorenz. If Lorenz was an engineer, he would not have made such a claim.) Therefore, Brazilian butterflies are fictional and unrealistic. For example, the Great Depression of the 1930s recovered in a short period, and the pandemic of the early 2020s spread rapidly and suddenly. However, the disease quickly returned to normal in just two years. 2.4.3. Redefinitions of Kuhn’s Structure of the Scientific Revolution (Background) The following example is Kuhn's theory of scientific innovation [ 18 ], proposed in 1963, which is widely known to the public. He argued that scientific revolutions consist of three stages: innovation, paradigm shifts, and normal science. For example, Galileo argued for heliocentric theory (innovation) in the Middle Ages, which has changed people's perceptions since the 15th century (paradigm shift). However, no one has questioned this (normal science), and Kuhn has solved this problem based on logical thinking. Paradoxically, if he had approached it with systems thinking, he would have reached a different conclusion. (Modeling and simulation): Most innovative inventions, such as automobiles, have evolved slowly. They slowly reduce production cost Q(s). Conversely, consumer utility and purchasing power H(s) increase slowly over time. In addition, the production cost and consumer purchasing power are inversely proportional, and the curves intersect, as shown in Fig. 2(c). Furthermore, this case could be simulated. When the damping factor β of the model system was close to 1, the output of the system was saturated in three stages, as shown in Fig. 5 (b). Consequently, scientific and technological innovation processes are expected to follow the exponential function as equation y(t) = 1 − e − xt , where x is a constant and t denotes time. His argument can be expressed as a simple time-series function: (Verification): Kuhn's scientific innovation process can be simulated in real-time. For example, automobile technology has developed slowly in three stages over the past 150 years, which can be reproduced in real-time. Other examples include steam engines, gunpowder, fertilizers, semiconductors, the internet, and mobile phones, all of which have become increasingly advanced and saturated. (Normal science) Unfortunately, these problems cannot be expressed quantitatively, because they are metaphysical. 3. Results The highlight of this study is as follow It presents a method for solving a complex system that has not been solved for 300 years. This is a dynamic problem that fluctuates over time and has been solved using a systematic solution in real time. A complex system such as an ecosystem is a closed-loop system that maintains equilibrium through self-regulation. It is modeled as a model system, as shown in Fig. 1 (b), and then solved using system analysis theory and simulation. Remarkably, the new solution does not overlap with the existing solution and does not conflict, so both solutions should be adopted [logical solution + systematic solution]; this is a very reasonable result. However, if physicists do not satisfy it to determinism, so they keep on maintain the old solution; there is no problem. 4. Discussions Above, this study shows that large-scale complex systems such as ecosystems have self-regulating functions that try to maintain their own equilibrium. Therefore, we modeled [complex systems] → as systems with dynamic characteristics → reproducing the dynamic characteristics through simulation. You should not doubt this experimental result. Because anyone can use it. Also, we do not need to abandon the chaos theory that we are using. Therefore, there is no reason to hesitate to adopt a logical solution or a systematic solution. [Note: Traditional physicists and systems scientists do not need to argue with each other because they approach the complexity shown by complex systems from different perspectives. Physicists can use chaos theory, and systems scientists can use a new solution.] Therefore, it is a wise choice to adopt all available solutions. Nevertheless, why do physicists not welcome new solutions? They misunderstood it as a replacement for the chaos theory. [Note: It seems that they cannot see the forest while looking at the trees]. Therefore, the systematic solution presented here will be provided first to other scientists who want it. Meanwhile, there is an issue that the researcher is deeply interested in regarding this study. This is the claim of Ilya Prigogine mentioned above. In 1997, he claimed the necessity of coexistence of [determinism and indeterminism] for traditional physicists and mathematicians who follow single determinism. This study proves the validity of this claim. He should then explain why traditional physicists ignored his assertions. On the other hand, we need to know what recently emerged AI is a typical system created based on systems thinking. The internal structure of the artificial intelligence is the same as that shown in Fig. 1 (b). It contains four elements in AI. It determines the optimal answer through repeated learning based on a large database. In this case, physicists and mathematicians must also be able to systematically approach participating in the research. Therefore, physicists and mathematicians should adopt systematic solutions based on systematic thinking. Please keep this in mind: If so, we should use the chaos theory that physicists have developed and used for over 300 years along with a new solution; [chaos theory + systematic solution]. Here, we present three well-known books on the chaos theory. The first is ‘Entropy’ [ 19 ] by economist Jeremy Rifkin. Ironically, if he approached it with systems thinking, he might have written a different book. Next is ‘At Home of the Universe’ [ 20 ] by Stuart Kauffman, who wrote it while working at the Santa Fe Institute [ 21 ], a research institute famous for its study of complex systems. The recent book ‘Simply Complexity’ [ 22 ] by physicist Neil Johnson is a thorough exploration of classical chaos theory and modern scientific research and presents the results. Finally, this study is a research result that should be dealt with by a systems scientist who is well versed in control theory. If the reader is a physicist, mathematician, or other scientist, he should learn the control theory and system analysis theory. This is because the systematic solution introduced in this study was difficult to digest. But do not worry. This is a complex and difficult mathematical solution, but it can be processed by the computer program MATLAB, and anyone can easily solve it. If you can use this solution, please refer to the application case in section 2.4 . 5. Conclusions This study presents a dynamic solution - a systematic solution for complex systems exhibiting nonlinearity and complexity. This is a groundbreaking solution for systems scientists. This is because it solves complex systems that have not been solved for years by using a dynamic method rather than a static method. In addition, there is no room for doubt because it has been proven with [modeling + simulation] that system scientists are familiar with. Physicists and mathematicians who view complex systems as static problems and solve them using chaos theory should not criticize them without reason. However, other scientists are encouraged to adopt both solutions [existing chaos theory + new systematic solution]; there is no restriction on this. In addition, if someone wants to verify the validity of the above solution, they can reproduce it using the above simulator. Hence, we hope that this study will contribute to the development of other sciences, such as systems science, traditional physics, and ecology. Declarations Availability of data : No data were generated during this study. Ethics approval and consent to participate: Not applicable. Competing interests : The authors declare no competing interests. Funding : Not applicable Authors’ contributions : Cha conceptualized and wrote this article, and Kim verified the process. All the authors have read and approved the final manuscript. Acknowledgments; Appreciate KG Engineering Co. This study was supported by them. We would like to thank Editage (www.editage.co.kr) for the English language editing. References Casti JL. Complexity: explain the paradoxical world through the science of surprise. New York: Harper Perennial; 1995. DDC 003.7 21 ISBN 00609258761. Arnold, Ross D., and Jon P. Wade. "A definition of systems thinking: A systems approach." Procedia computer science 44 (2015): 669-678. https://doi.org/10.1016/j.procs.2015.03.050 GSE and GORS Seminar Report. What is a systems incident? GSE and GORS Seminar Report. Official Live. July 3, 2012. Office of Science and Government. https://corporatefinanceinstitute.com/resources/knowledge/strategy/systems-thinking/. Cha, DS, Jun HJ. The Origin of Nonlinear Dynamics Involving Complexity in Modern Sciences. 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Springer Science & Business Media, 2013. https://books.google.co.kr/books?hl=ko&lr=&id=N_jZBwAAQBAJ&oi=fnd&pg=PA1&dq=laplace+transform&ots=m2TbuVPkOF&sig= EUwvvXtcIdfRNxG_HjHdVK1Gf7A&redir_esc=y#v=onepage&q=laplace%20transform&f=false MATLAB-Simulink. MathWorks. Available from: https://kr.mathworks.com/products/simulink.html?s_tid=hp_products_simulink . Video clips. Available from: https://www.youtube.com/watch?v=DrfyX9o3x7A Logistic function. Wikipedia. Available from: https://en.wikipedia.org/wiki/Logistic_function#Logistic_differential_equation Lorenz, Edward. "The butterfly effect." World Scientific Series on Nonlinear Science Series A 39 (2000): 91-94. book Thomas K. The structure of scientific revolutions. Chicago: University of Chicago Press; 2012. ISBN10:0226458121. Jeremy R. Entropy: a new worldview. New York: Viking Adults; 1981. ISBN10: 9780670297177. Stuart K. House of the universe: a search for the law of self-organization and complexity. Oxford: Oxford University Press; 1996. ISBN-10: 0195111303. Santa Fe Research Institute. Available from: https://www.santafe.edu/about/overview. Accessed 10 Jun 2022. Neil J. Simply complexity. Oxford: One-World Publications; 2009. ISBN-10: ‎ 9781851686308 Additional Declarations No competing interests reported. Supplementary Files Appendix.docx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6101727","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":435237178,"identity":"7e67a16a-6f91-4ba1-a818-9f4915b0042a","order_by":0,"name":"Deok soo Cha","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAvElEQVRIiWNgGAWjYDACCQYDIGmTAOYkFBCvJS2BgQ2kxYB4LYchWhiI0cI/u3nzhw8V5/P45bsTPzwwYJDnFztAwJI7x8okZ5y5XSzZxrtZAugww5mzE/BrMZDIMWPmbbuduOEY7waQlgSD24S1GH/mbTsH0rL5B7FaDKR52w6AtGwjzhaJG2kgvyQnzmzL3WaRYCBB2C/8M5JBIWaX2M98dvPNHxU28vzSBLRg2Eqa8lEwCkbBKBgF2AEAtBNCOh4iXGoAAAAASUVORK5CYII=","orcid":"","institution":"Soong-sil University","correspondingAuthor":true,"prefix":"","firstName":"Deok","middleName":"soo","lastName":"Cha","suffix":""},{"id":435237179,"identity":"0dc2bf63-09db-42f2-b887-f0b6a051b8b3","order_by":1,"name":"kyoun il Kim","email":"","orcid":"","institution":"Chung-Ang University","correspondingAuthor":false,"prefix":"","firstName":"kyoun","middleName":"il","lastName":"Kim","suffix":""}],"badges":[],"createdAt":"2025-02-25 05:53:18","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6101727/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6101727/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":79564166,"identity":"6a78b9ee-b5ce-4b6f-b2b2-569665c74f92","added_by":"auto","created_at":"2025-03-31 09:10:34","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":26066,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Overview of the system; [Wikipedia - system] \u003cdel\u003e\u0026nbsp;\u003c/del\u003e(b) Block diagram of closed loop system; [The output has the inherent characteristic of always converging to zero.]\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/b0ac18d24792d177242f6dd2.jpg"},{"id":79563123,"identity":"c885be35-3b32-47fb-b327-72f24683896f","added_by":"auto","created_at":"2025-03-31 09:02:35","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":74044,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/13867a8d3b230326dbf4c98d.jpg"},{"id":79564167,"identity":"9bdf5895-b0a9-4fed-b6b1-fe59f33b4ce1","added_by":"auto","created_at":"2025-03-31 09:10:35","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":73839,"visible":true,"origin":"","legend":"\u003cp\u003eSee image above for figure legend\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/4c6fcb269e1aaa6580586012.jpg"},{"id":79563124,"identity":"47bc1c0e-350a-4d5a-bed3-2a82e180bc80","added_by":"auto","created_at":"2025-03-31 09:02:35","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":60577,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Dedicated systems simulator based on Eq. (3) (b) The output in screen - the response of basic function (c) The output in screen - the response of random function; video clip;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eULR https://www.youtube.com/watch?v=DrfyX9o3x7A\u0026amp;feature=youtube.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/18e208a0063a1e6ce5532e6c.jpg"},{"id":79563125,"identity":"b7344a13-b219-490c-bde6-abf8691069cc","added_by":"auto","created_at":"2025-03-31 09:02:35","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":57203,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Configuration of internal systems simulator based on Eq. (2). (b) Initial\u003cstrong\u003e \u003c/strong\u003ephenomena of system output. (c) Kuhn's scientific innovations process (invention – paradigm shift – normal science)\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/81b301ba221fc072725a3420.jpg"},{"id":86137425,"identity":"a63954c1-605e-461a-a9ec-ae9c6dd2ab23","added_by":"auto","created_at":"2025-07-07 07:55:21","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":865632,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/73d9bcf5-a822-4fbd-9d34-45f15731cae7.pdf"},{"id":79563121,"identity":"66bd34ea-6e2b-4077-8fc2-6e742ffafb74","added_by":"auto","created_at":"2025-03-31 09:02:34","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":16622,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-6101727/v1/782da6148726a1e1b2ed7aff.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Complex Systems Must Be Solved with Systematic Solution; How can We Solve Systematic Problem Such as Ecosystems Using Systematic Solution Dynamically","fulltext":[{"header":"Article Highlight","content":"\u003cp\u003e\u0026bull; \u0026nbsp;This study succeeded in solving complex systems that exhibit\u0026nbsp;nonlinear dynamics and complexity\u0026nbsp;by using a new systematic\u0026nbsp;solution based on systems thinking.\u003c/p\u003e\n\u003cp\u003e\u0026bull; \u0026nbsp;It is a new systematic solution that does not overlap and contradicts the logical solution (chaos theory). Therefore, we should adopt both logical and systematic solutions.\u003c/p\u003e\n\u003cp\u003e\u0026bull; \u0026nbsp;It can be proved and simulated in real time through [modeling + simulation] using MATLAB or a simulator\u003c/p\u003e"},{"header":"1. Introduction","content":"\u003cp\u003eThis paper aims to find and publish a solution to the complex system that has not been solved yet. The method has been treated as a static problem for a long time, but in this paper, unlike that, it is considered as a dynamic problem that changes over time and is solved in real time using a recently appeared systematic solution. In other words, this study presents a dynamic solution for complex systems that exhibit nonlinear dynamics and complexity [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] in nature, such as ecosystems and economic systems. Then, this research result will be provided to systems scientists and other scientists, including deterministic physicists. Before beginning, this study presents two suggestions for readers.\u003c/p\u003e \u003cp\u003eFirst, I hope that readers decide whether to adopt the results of this study. If readers think that the new solution here is reasonable, I hope that they will choose it without hesitation. If not, I hope that they will continue to use the chaos theory of statistical physics, which has been used for the past 300 years. There are no problems and no one will be harmed. Next, this study cites the theory of system analysis in the control theory as a mathematical tool. Physicists need prior knowledge of this issue. [Note: This mathematical tool was created by engineers in the 20th century, but was not used because traditional physics contradicts determinism.] \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eHere is a special comment. This paper asked various questions to the AI ​​system and received them, but the ones that were specifically mentioned here were marked.\u003c/span\u003e\u003c/p\u003e \u003cp\u003eIn the 20th century, complex systems were one of the most difficult problems in science. [Black holes/solar magnetism/superconductivity/nuclear theory/nuclear fusion/plasma/turbulence/climate change/complex systems/consciousness] It includes seven millennium mathematical problems that scientists are trying to solve. We will try to solve the ninth complex system among the ten that are difficult for anyone to solve. The method is to investigate the reason why complex systems are not solved and to solve them by utilizing the dynamic system characteristics of complex systems such as ecosystems or stock markets that fluctuate over time. This method has not been reported previously.\u003c/p\u003e \u003cp\u003eTo succeed in solving this problem, we must first understand why scientists have not been able to solve complex systems for 300 years. As a result of the investigation, the following conclusions were reached. Although both physicists and non-physicists (especially systems scientists) study complex systems as their research goals, they approach them using different academic methods. In addition, physicists approach the nonlinearity and complexity exhibited by complex systems based on determinism as an object (black box), but ignore the dynamic characteristics and self-regulating functions hidden in the system. This is why physicists have not been able to solve these problems. [Note; They have already rejected to adopt it, claiming that the solution is beyond the scope of physics and mathematics. ('23.11. 04, '24.04. 04) Then, physicists should not approach this research.]\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e Next, systems scientists state that complex systems are not free from determinism. They see the self-regulating function as difficult to handle in a dynamic way. Instead, they build a precise simulator of all dynamic systems and reproduce them repeatedly to solve the complex system by [modeling and simulation]. A representative case is the system dynamics. [Note: This is a useful solution, but it is imperfect. Consequently, no one has been able to solve complex problems for 300 years]. However, we did not need to worry about this. We can solve this problem without a static solution that is considered to be stationary, but with a dynamic solution that changes over time. However, this solution cannot be found in deterministic physics. It is a solution that can simultaneously see both forests and trees at the same time. The solution is presented in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. [Remark; The 'Note' inserted in this paper is inserted for the reviewer. It will be removed.]\u003c/p\u003e"},{"header":"2. Martials and Methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Scientific Background\u003c/h2\u003e \u003cp\u003eThis section presents a method to consider complex systems as closed-loop systems and solve them dynamically. If readers approach complex systems as objects like deterministic physicists and view them as static problems, they will have difficulty understanding this solution. In that case, they can use existing chaos theory and there will be no problem. I hope there is no misunderstanding. However, if readers are systems scientists, they will have no difficulty understanding this solution.\u003c/p\u003e \u003cp\u003eFor example, this is like an internist appearing in the Middle Ages when there were only surgeons or the appearance of an electric car in a world where there were only engine cars. This is the ideal relationship. In the future, we should follow (logical solution\u0026thinsp;+\u0026thinsp;systematic solution): [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] [Note; If physicists and mathematicians have been misunderstood as replacing their existing solutions with a new systematic solution, other scientists have no reason to receive their consent. However, it has nothing to do with other scientists].\u003c/p\u003e \u003cp\u003ePreliminary Knowledge; Here: For scientists other than system scientists, it is necessary to explain what a systematic solution is. [Note: Please check here what the difference between a \u0026lsquo;systemic\u0026rsquo; solution (analyzing the entire system and find a basic solution.) and a 'systematic solution' is; Chat GPT] This can be explained with Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a\u0026ndash;b). A system scientist including other scientists understand that the ecosystem (stock market) in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(a) can be replaced by a dynamic system consisting of four elements: input U(s), process Q(s), feedback H(s), and output Y(s), as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b). [Note: This is also consistent with the internal structure of AI systems]. In particular, if feedback H(s) in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b) does not exist, it is an open-loop system. This is an algebraic problem and is not called a system. In other case, if H(s) exists, the system is a self-regulating system, such as an ecosystem. In this case, there are active and passive elements inside, and the sum of the two elements continuously converges to zero (energy conservation) The basic model system is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b).\u003c/p\u003e \u003cp\u003eHistorical background: According to the literature review results [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e][\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e], there has been no case of defining and dynamically solving complex systems as systematic problems based on systems thinking for the past 300 years. A more obvious reason is that physicists have treated them as black boxes based on determinism. [Note: Determinism in physics has not treated non-reversible, non-measurable, and non-reproducible problems.] On the other hand, systems scientists have understood that complex systems are closed-loop systems owing to the influence of determinism, but have not been able to convert and solve them as closed-loop systems with self-regulating functions, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b). This paper presents the methods in this study. Fortunately, however, systems analysis theory appeared in the 20th century, so any scientist who understood it can solve it.\u003c/p\u003e \u003cp\u003eConsequently, in 2024, a third-party scientist succeeded in solving the complex system dynamically in real time. If we can successfully solve this complex system, what can we gain from it? The results are also non-quantitative and non-qualitative, but they can help us understand the source of the complexity and predict the trends. However, this research was completed by a non-physicist and not a physicist. Likewise, there are cases where non-physicists, not physicists, have studied complex systems. A representative example is the Ilya Prigogine, a Nobel Prize winner. He is an expert in complexity. About 30 years ago, in 1997, he presented a very important conclusion in 'The End of Certainty' [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]: [Determinism must coexist with indeterminism], and Nobel Prize winner Murray Gell-Mann also agreed with this assertion. However, most physicists and mathematicians ignore his prediction, but other scientists will prove his assertion in 2025, and we should pay tribute to him.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e Complex systems are characterized by systematic problems. [Chat GPT] If so, then most systems scientists except determinists can understand this, because they dynamically approach the system. If we understand this, we first need to understand the internal structure of a system with self-regulating capabilities, such as a food chain in an ecosystem. According to the literature, a system is defined as \"a set of interacting or interrelated elements that operate according to a set of rules to form an integrated whole.\" However, it is missing self-regulating functions is determinism. Therefore, if we assume a system to be a time-series function, we can solve this very easily.\u003c/p\u003e \u003cp\u003eFor example, autonomous speed control of a steam locomotive is the application of a self-regulating system. It maintains a constant speed using a device (governor) that combines an element that tries to increase speed and a feedback element that is inversely proportional to the speed. (See the \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003eAppendix\u003c/span\u003e.) This is explained by the [demand and supply curve] [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] in economics, as shown in Fig.\u0026nbsp;2(c). If the two entropy curves (supply and demand) both increase, the two curves intersect. In this case, because the two elements have a time difference d, the intersection point will move left and right endlessly. As a result, the market price will move endlessly over time to converge to equilibrium and eventually converge to a constant price [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]; [Note: Adam Smith's invisible hand. This is why the huge and complex natural world maintains equilibrium (stability).]\u003c/p\u003e \u003cp\u003eIn this case, it is modeled as a feedback system, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b), and solved using system analysis theory, as shown in Fig.\u0026nbsp;2(a) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. However, many scientists are concerned about how to model large, complex, and difficult-to-solve economic and social phenomena as a basic model system, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b). [Note; The system analysis theory suggests a method to simplify and model even the most complex system as a single basic system, so there is no need to be appropriate at all.] Moreover, there is no difficulty because the analysis process can be performed using a computer or simulator.\u003c/p\u003e \u003cp\u003eTo improve our understanding, we applied the self-regulating function mentioned above to the ecosystem. As mentioned above, it can be divided into active and passive elements in the food chain, such as predator q(t) and prey h(t). The two elements are in the same space; therefore, both increasing curves intersect each other, such as the demand and supply curves in Fig.\u0026nbsp;2(c). However, there was a delay between the two. [Note: This requires the growth time of organisms in an ecosystem.] In this case, the following equation must be satisfied:\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$$\\:d/dt\\left\\{q\\right(t)+h(t-d\\left)\\right\\}=0\\:$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e[Note; This equation is used to find the case where the sum of the number of predators q(t) and the number of prey h(t) is minimum (zero); this is because the system tries to maintain equilibrium. Then, we can model it as a system with the same mechanism as the feedback system. This is the highlight. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003e[Note; If anyone cannot understand the meaning of the above equation, they cannot solve the systematic solution.]\u003c/span\u003e\u003c/p\u003e \u003cp\u003eAs a result, we can model the ecosystem as a basic system, as shown in Fig.\u0026nbsp;2(d). This paper will then reproduce the complexity that actually appears in the ecosystem based on the explanation so far. Note that physicists and mathematicians cannot criticize this because it is something that systems scientists should solve. Determinists who regarded the system as a black box were excluded.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Process of Modeling and Simulations\u003c/h2\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.3.1. Modeling\u003c/h2\u003e \u003cp\u003eThis study explains why scientists have not been able to solve complex systems in a new manner. As a result, if someone succeeds in modeling a complex system such as an ecosystem, as shown in Fig.\u0026nbsp;2(d), they can reproduce the complexity and nonlinearity through experiments. [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/p\u003e \u003cp\u003eof the size of the ecosystem, stock market, or social phenomena, it can be transformed into a basic system, as shown in Fig.\u0026nbsp;2(d). [Note: For this method, refer to the control theory textbook.] The transfer function (parameter) of the model system is expressed as equations (\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) and (2) below: This is described using the Laplace operator [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e], which replaces the complex differential equation. [Note; For the reason for using the Laplace transform here and the specific method, refer to the textbook or Chat GPT.]; Specifically, [s] represents the Laplace operator for solving the time-series function, β represents the damping coefficient of the system, and ω represents the natural frequency.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:\\begin{array}{c}\\:\\:\\\\\\:\\:\\:output\\:Y\\left(s\\right)=parameter\\:F\\left(s\\right)\\bullet\\:input\\:U\\left(s\\right)\\:\\:\\:\\:\\end{array}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:F\\left(s\\right)=\\frac{Y\\left(s\\right)}{U\\left(s\\right)}=\\frac{G\\left(s\\right)}{1+G\\left(s\\right)H\\left(s\\right)}=\\frac{{\\omega\\:}^{2}}{{s}^{2}+2\\beta\\:\\omega\\:s+{\\omega\\:}^{2}}\\)\u003c/span\u003e \u003c/span\u003e \u0026rarr; example (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\frac{1}{\\:{s}^{2}+0.4s+1}\\:)\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:=0.2\\)\u003c/span\u003e\u003c/span\u003e (2)\u003c/p\u003e \u003cp\u003e(Commentary) If you are a system scientist, Eq.\u0026nbsp;(2) is the parameter (transfer function) of all dynamic systems existing in nature. Solving this problem manually is extremely complex and difficult. In this case, the output of the complex system can be reproduced, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b), using the commercial program MATLAB [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e], as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a). (the virtual transfer function at this time is \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F\\left(s\\right)=1/(s^2+0.4s+1)\\)\u003c/span\u003e\u003c/span\u003e ) Finally, by applying the above two equations to solve the output of the model system in Fig.\u0026nbsp;2(d) though the Laplace reverse transform, we obtained the result in Eq.\u0026nbsp;(3), which represents the response generated when a basic function [Note: unit step function is defined as: if t=0, u(t)=0; if t\u0026gt;0, u(t)=1) is applied. The output of the dynamic systems is highlighted in this study.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv id=\"Equb\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$$\\:{Y\\left(s\\right)}^{-1}=y\\left(t\\right)=1-A\\bullet\\:{e}^{-B\\:\\bullet\\:\\:t}{sin}\\begin{array}{c}\\:\\:\\\\\\:\\:\\left(W\\:\\bullet\\:\\:t\\:+\\:\\phi\\:\\right)\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(3\\right)\\end{array}$$\u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Equc\" class=\"Equation\"\u003e \u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$$\\:{where},\\begin{array}{c}\\:\\:\\\\\\:\\:\\:\\left[\\:A=\\frac{1}{\\sqrt{1-{\\beta\\:}^{2}}},\\:\\:\\:B=\\beta\\:\\omega\\:,\\:\\:W=\\omega\\:\\sqrt{1-{\\beta\\:}^{2}\\:},\\:\\:\\phi\\:={{cos}}^{-1}\\beta\\:\\:\\right]\\end{array}$$\u003c/div\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003eIf you are a systems scientist or a scientist who understands control theory, you will understand that Eq.\u0026nbsp;(3) is the fundamental response that all systems exhibit. This overlaps exponential and periodic functions. Therefore, it implements periodicity, self-organization, and initial phenomena, and if a random function is input, irregularity is added to the output, thereby exhibiting typical complexity. Please refer to Figs.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) and 3(b).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eULR \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.youtube.com/watch?v=DrfyX9o3x7A\u0026amp;feature=youtube\u003c/span\u003e\u003cspan address=\"https://www.youtube.com/watch?v=DrfyX9o3x7A\u0026amp;feature=youtube\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.3.2. Experiment - Computer and Analog Simulator\u003c/h2\u003e \u003cp\u003eThis paper introduces a method to reproduce the complex system in the above section on a computer, and presents the results in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e(b). It can be observed that the input and output are irreversible. Because anyone can reproduce this using the MATLB program, I recommend that you try it yourself. However, there is an analog simulator that is more realistic than the computer simulation above, and reproduces accurate results in real time [Note: The internal structure of the simulator is shown in Figure. 5(a)]. We can confirm The response to the basic function was confirmed, as shown in Figure. 4(b), and the response to the random function, as shown in Figure. 4(c). Paradoxically, this figure shows that complex systems are systematic problems.\u003c/p\u003e \u003cp\u003e(Verification) By randomly changing the inputs of the above model system and observing the output over a long period of time, we can discover the complexity in its output; unique characteristics of complex system outputs, such as irregularity, regularity, self-organization, and initial phenomena, can be observed. A video clip has been provided to illustrate this process [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]. \u003cspan type=\"Underline\" class=\"Underline\" name=\"Emphasis\"\u003eThrough this approach, we reproduce nonlinear dynamics and complexity, demonstrating that these are not algebraic (logical) issues\u003c/span\u003e, but systematic challenges.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Application Examples \u003c/h2\u003e \u003cp\u003eTo prove the new solution, this study presents three application cases, which illustrate a comparison between existing algebraic solutions and the proposed systematic solutions.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.4.1 Re-definitions of Logistic Curve in Ecology\u003c/h2\u003e \u003cp\u003e(Background): The first is the logistic curve in common sense [Note: This is a famous theory; therefore, only the results are presented. [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] This is the logistic curve, and the function is defined as \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:F\\left(s\\right)=\\frac{1}{{1+e}^{-x}\\:}\\)\u003c/span\u003e\u003c/span\u003e. It is expressed as a finite function in the static state. As is already known, Verhulst intuitively recognized that population growth and decline are periodic, and based on this, devised a sigmoid function and curve [S].\u003c/p\u003e \u003cp\u003e(Modeling and simulation): However, this is not an ideal solution because it is not a static problem; we solved it as a dynamic problem in real-time. For example, can be determined using Eq.\u0026nbsp;(3), which shows the output of the ecosystem model. If the damping factor of the equation has no damping (β\u0026thinsp;=\u0026thinsp;0), then the output of Eq.\u0026nbsp;(3) is determined as a periodic function y(t)\u0026thinsp;=\u0026thinsp;1 \u0026ndash; sin (ωt). This is a periodic function with a frequency ω. If this is represented as a dimensionless graph, we obtain a sigmoid [S] curve.\u003c/p\u003e \u003cp\u003e(Verification) Given that the population growth of an ecosystem is a dynamic problem, it must be solved in real-time. Thus, it initially grows exponentially, then gradually saturates, and exhibits a sine curve that repeatedly increases or decreases along the curve.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.4.2. Redefinitions of Lorenz\u0026rsquo;s Butterfly Effect\u003c/h2\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(Background) A representative example is Lorenz's butterfly effect [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], which is part of the chaos theory created by statistical physicists. This claim was first made in 1963, just 80 years ago, and has remained unchanged since then. However, this can be resolved using Eq.\u0026nbsp;(3), as presented above.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e(Modeling and simulation): Model the ecosystem (stock market) as a model system, as shown in Fig.\u0026nbsp;2(d), and assume that its output function is as shown in Eq.\u0026nbsp;(3). In this case, if the damping factor β included in the transfer function of the model system is underdamped, the initial output of the model system overshoots, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b), similar to a lightning surge. However, there is no problem because the overshoot increases rapidly, but disappears momentarily and returns to the original state. This is a unique property of all the dynamic systems.\u003c/p\u003e \u003cp\u003e(Verification): This experimental result differs from that of Lorenz. If Lorenz was an engineer, he would not have made such a claim.) Therefore, Brazilian butterflies are fictional and unrealistic. For example, the Great Depression of the 1930s recovered in a short period, and the pandemic of the early 2020s spread rapidly and suddenly. However, the disease quickly returned to normal in just two years.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e2.4.3. Redefinitions of Kuhn\u0026rsquo;s Structure of the Scientific Revolution\u003c/h2\u003e \u003cp\u003e(Background) The following example is Kuhn's theory of scientific innovation [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], proposed in 1963, which is widely known to the public. He argued that scientific revolutions consist of three stages: innovation, paradigm shifts, and normal science. For example, Galileo argued for heliocentric theory (innovation) in the Middle Ages, which has changed people's perceptions since the 15th century (paradigm shift). However, no one has questioned this (normal science), and Kuhn has solved this problem based on logical thinking. Paradoxically, if he had approached it with systems thinking, he would have reached a different conclusion.\u003c/p\u003e \u003cp\u003e(Modeling and simulation): Most innovative inventions, such as automobiles, have evolved slowly. They slowly reduce production cost Q(s). Conversely, consumer utility and purchasing power H(s) increase slowly over time. In addition, the production cost and consumer purchasing power are inversely proportional, and the curves intersect, as shown in Fig.\u0026nbsp;2(c). Furthermore, this case could be simulated. When the damping factor β of the model system was close to 1, the output of the system was saturated in three stages, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e(b). Consequently, scientific and technological innovation processes are expected to follow the exponential function as equation y(t)\u0026thinsp;=\u0026thinsp;1\u0026thinsp;\u0026minus;\u0026thinsp;e\u003csup\u003e\u0026minus;\u0026thinsp;xt\u003c/sup\u003e, where x is a constant and t denotes time. His argument can be expressed as a simple time-series function:\u003c/p\u003e \u003cp\u003e(Verification): Kuhn's scientific innovation process can be simulated in real-time. For example, automobile technology has developed slowly in three stages over the past 150 years, which can be reproduced in real-time. Other examples include steam engines, gunpowder, fertilizers, semiconductors, the internet, and mobile phones, all of which have become increasingly advanced and saturated. (Normal science) Unfortunately, these problems cannot be expressed quantitatively, because they are metaphysical.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"3. Results","content":"\u003cp\u003eThe highlight of this study is as follow\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eIt presents a method for solving a complex system that has not been solved for 300 years. This is a dynamic problem that fluctuates over time and has been solved using a systematic solution in real time.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eA complex system such as an ecosystem is a closed-loop system that maintains equilibrium through self-regulation. It is modeled as a model system, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b), and then solved using system analysis theory and simulation.\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eRemarkably, the new solution does not overlap with the existing solution and does not conflict, so both solutions should be adopted [logical solution\u0026thinsp;+\u0026thinsp;systematic solution]; this is a very reasonable result.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003eHowever, if physicists do not satisfy it to determinism, so they keep on maintain the old solution; there is no problem.\u003c/p\u003e"},{"header":"4. Discussions","content":"\u003cp\u003eAbove, this study shows that large-scale complex systems such as ecosystems have self-regulating functions that try to maintain their own equilibrium. Therefore, we modeled [complex systems] \u0026rarr; as systems with dynamic characteristics \u0026rarr; reproducing the dynamic characteristics through simulation. You should not doubt this experimental result. Because anyone can use it. Also, we do not need to abandon the chaos theory that we are using. Therefore, there is no reason to hesitate to adopt a logical solution or a systematic solution. [Note: Traditional physicists and systems scientists do not need to argue with each other because they approach the complexity shown by complex systems from different perspectives. Physicists can use chaos theory, and systems scientists can use a new solution.]\u003c/p\u003e \u003cp\u003eTherefore, it is a wise choice to adopt all available solutions. Nevertheless, why do physicists not welcome new solutions? They misunderstood it as a replacement for the chaos theory. [Note: It seems that they cannot see the forest while looking at the trees]. Therefore, the systematic solution presented here will be provided first to other scientists who want it. Meanwhile, there is an issue that the researcher is deeply interested in regarding this study. This is the claim of Ilya Prigogine mentioned above. In 1997, he claimed the necessity of coexistence of [determinism and indeterminism] for traditional physicists and mathematicians who follow single determinism. This study proves the validity of this claim. He should then explain why traditional physicists ignored his assertions.\u003c/p\u003e \u003cp\u003eOn the other hand, we need to know what recently emerged AI is a typical system created based on systems thinking. The internal structure of the artificial intelligence is the same as that shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b). It contains four elements in AI. It determines the optimal answer through repeated learning based on a large database. In this case, physicists and mathematicians must also be able to systematically approach participating in the research. Therefore, physicists and mathematicians should adopt systematic solutions based on systematic thinking. Please keep this in mind:\u003c/p\u003e \u003cp\u003eIf so, we should use the chaos theory that physicists have developed and used for over 300 years along with a new solution; [chaos theory\u0026thinsp;+\u0026thinsp;systematic solution]. Here, we present three well-known books on the chaos theory. The first is \u003cem\u003e\u0026lsquo;Entropy\u0026rsquo;\u003c/em\u003e [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] by economist Jeremy Rifkin. Ironically, if he approached it with systems thinking, he might have written a different book. Next is \u003cem\u003e\u0026lsquo;At Home of the Universe\u0026rsquo;\u003c/em\u003e [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] by Stuart Kauffman, who wrote it while working at the Santa Fe Institute [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e], a research institute famous for its study of complex systems. The recent book \u003cem\u003e\u0026lsquo;Simply Complexity\u0026rsquo;\u003c/em\u003e [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] by physicist Neil Johnson is a thorough exploration of classical chaos theory and modern scientific research and presents the results.\u003c/p\u003e \u003cp\u003eFinally, this study is a research result that should be dealt with by a systems scientist who is well versed in control theory. If the reader is a physicist, mathematician, or other scientist, he should learn the control theory and system analysis theory. This is because the systematic solution introduced in this study was difficult to digest. But do not worry. This is a complex and difficult mathematical solution, but it can be processed by the computer program MATLAB, and anyone can easily solve it. If you can use this solution, please refer to the application case in section \u003cspan refid=\"Sec7\" class=\"InternalRef\"\u003e2.4\u003c/span\u003e.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eThis study presents a dynamic solution - a systematic solution for complex systems exhibiting nonlinearity and complexity. This is a groundbreaking solution for systems scientists. This is because it solves complex systems that have not been solved for years by using a dynamic method rather than a static method. In addition, there is no room for doubt because it has been proven with [modeling\u0026thinsp;+\u0026thinsp;simulation] that system scientists are familiar with. Physicists and mathematicians who view complex systems as static problems and solve them using chaos theory should not criticize them without reason. However, other scientists are encouraged to adopt both solutions [existing chaos theory\u0026thinsp;+\u0026thinsp;new systematic solution]; there is no restriction on this. In addition, if someone wants to verify the validity of the above solution, they can reproduce it using the above simulator. Hence, we hope that this study will contribute to the development of other sciences, such as systems science, traditional physics, and ecology.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAvailability of data\u003c/strong\u003e\u003cstrong\u003e:\u0026nbsp;\u003c/strong\u003eNo data were generated during this study.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval and consent to participate:\u003c/strong\u003e Not applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e: The authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Not applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026rsquo; contributions\u003c/strong\u003e: Cha conceptualized and wrote this article, and Kim verified the \u0026nbsp;process. All the authors have read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments;\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003eAppreciate KG Engineering Co. This study was supported by them. We would like to thank Editage (www.editage.co.kr) for the English language editing.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eCasti JL. Complexity: explain the paradoxical world through the science of surprise. New York: Harper Perennial; 1995. DDC 003.7 21 ISBN 00609258761. \u003c/li\u003e\n\u003cli\u003eArnold, Ross D., and Jon P. Wade. \u0026quot;A definition of systems thinking: A systems approach.\u0026quot; Procedia computer science 44 (2015): 669-678.\u003cbr\u003ehttps://doi.org/10.1016/j.procs.2015.03.050\u003cbr\u003eGSE and GORS Seminar Report. What is a systems incident? GSE and GORS Seminar Report. Official Live. July 3, 2012. Office of Science and Government. https://corporatefinanceinstitute.com/resources/knowledge/strategy/systems-thinking/.\u003c/li\u003e\n\u003cli\u003eCha, DS, Jun HJ. The Origin of Nonlinear Dynamics Involving Complexity in Modern Sciences. Open Journal of Applied Sciences 10.10 (2020): 654.\u003cbr\u003ehttps://scholar.google.li/scholar?hl=ko\u0026amp;as_sdt=0%2C5\u0026amp;q=The+origin+of+nonlinear+dynamics+involving+complexity+in+modern+sciences\u0026amp;btnG= \u003c/li\u003e\n\u003cli\u003eMotz L, Hane JW. The story of physics. New York: Springer; 1989. ISBN: 0306430762.\u003c/li\u003e\n\u003cli\u003eBall P. Critical mass: how one thing leads to another. 1st ed. New York: Farrar, Straus and Giroux; 2004. First Edition ISBN-10: 0374281254 ISBN-13: \u0026lrm;978-0374281250\u003c/li\u003e\n\u003cli\u003ePrigogine, Ilya, and Isabelle Stengers. The end of certainty. Simon and Schuster, 1997.\u003cbr\u003ehttps://scholar.google.li/scholar?hl=ko\u0026amp;as_sdt=0%2C5\u0026amp;q=The+end+of+certainty\u0026amp;btnG=#d=gs_cit\u0026\u003cbr\u003eamp;t=1732630399425\u0026amp;u=%2Fscholar%3Fq%3Dinfo%3Ai_Nh55H_nFEJ%3Ascholar.google.com%2F%26output%3Dcite%26scirp%3D0%\u003cbr\u003e26hl%3Dko \u003c/li\u003e\n\u003cli\u003eMarwala, Tshilidzi, et al. \u0026quot;Supply and demand.\u0026quot; Artificial Intelligence and Economic Theory: Skynet in the Market (2017): 15-25.\u003cbr\u003ehttps://link.springer.com/chapter/10.1007/978-3-319-66104-9_2\u003c/li\u003e\n\u003cli\u003eCha DS. Investigative report for economists; prediction of stock market and functional invisible hand and law of supply and demand. Theor Econ Lett. 2016;6(6):1427\u0026ndash;37.10.4236/tel.2016.66120 \u003c/li\u003e\n\u003cli\u003eCha DS, Kim KI. New systematic solutions for solving nonlinear dynamics using systems analysis theory based on engineering science. Mod Appl Sci. 2021;15(6):46\u0026ndash;55. 10.5539/mas.v15n6p46.\u003c/li\u003e\n\u003cli\u003eKuo, Benjamin C. Automatic control systems. Prentice Hall PTR, 1987.\u003cbr\u003e https://dl.acm.org/doi/abs/10.5555/535813 \u003c/li\u003e\n\u003cli\u003eKim KI. Automatic control engineering. Seoul: Seong-andang; 2018. ISBN 9788931525670.\u003c/li\u003e\n\u003cli\u003eCha DS. Establishment of new solution for complex systems in multidisciplinary science based on feedback system analysis method and proven by simulator. J Mod Phys. 2015;6(13):1927\u0026ndash;34. \u003cu\u003e10.4236 / jmp.2015.613198.\u003c/u\u003e\u003c/li\u003e\n\u003cli\u003eSchiff, Joel L. The Laplace transform: theory and applications. Springer Science \u0026amp; Business Media, 2013.\u003cbr\u003e https://books.google.co.kr/books?hl=ko\u0026amp;lr=\u0026amp;id=N_jZBwAAQBAJ\u0026amp;oi=fnd\u0026amp;pg=PA1\u0026amp;dq=laplace+transform\u0026amp;ots=m2TbuVPkOF\u0026amp;sig=\u003cbr\u003eEUwvvXtcIdfRNxG_HjHdVK1Gf7A\u0026amp;redir_esc=y#v=onepage\u0026amp;q=laplace%20transform\u0026amp;f=false\u003c/li\u003e\n\u003cli\u003eMATLAB-Simulink. MathWorks. Available from: https://kr.mathworks.com/products/simulink.html?s_tid=hp_products_simulink\u003cu\u003e.\u003c/u\u003e\u003c/li\u003e\n\u003cli\u003eVideo clips. Available from:\u003cu\u003e \u003c/u\u003ehttps://www.youtube.com/watch?v=DrfyX9o3x7A \u003c/li\u003e\n\u003cli\u003eLogistic function. Wikipedia. Available from: https://en.wikipedia.org/wiki/Logistic_function#Logistic_differential_equation\u003c/li\u003e\n\u003cli\u003eLorenz, Edward. \u0026quot;The butterfly effect.\u0026quot; World Scientific Series on Nonlinear Science Series A 39 (2000): 91-94. book\u003c/li\u003e\n\u003cli\u003eThomas K. The structure of scientific revolutions. Chicago: University of Chicago Press; 2012. ISBN10:0226458121. \u003c/li\u003e\n\u003cli\u003eJeremy R. Entropy: a new worldview. New York: Viking Adults; 1981. ISBN10: 9780670297177.\u003c/li\u003e\n\u003cli\u003eStuart K. House of the universe: a search for the law of self-organization and complexity. Oxford: Oxford University Press; 1996. ISBN-10: 0195111303.\u003c/li\u003e\n\u003cli\u003eSanta Fe Research Institute. Available from: https://www.santafe.edu/about/overview. Accessed 10 Jun 2022.\u003c/li\u003e\n\u003cli\u003eNeil J. Simply complexity. Oxford: One-World Publications; 2009. ISBN-10: \u0026lrm; 9781851686308\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"dynamic systems, systems thinking, chaos theory, nonlinear dynamics","lastPublishedDoi":"10.21203/rs.3.rs-6101727/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6101727/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study presents a complete solution using a different method from the chaos theory currently used to solve complex systems; therefore, the reader must decide whether to choose it. Over the past 300 years, complex systems with non-quantitative and non-qualitative characteristics, such as ecosystems, have been solved using the chaos theory of statistical physics based on vertical (logical) thinking. However, the new solution is completely new because it is dynamically solved. In other words, unlike the existing one, the new solution views the complex system as a systematic problem that fluctuates endlessly over time and solves it in real time using a systematic solution based on systems thinking with the theory of system analysis that emerged in the 20th century. To solve this problem, we used a method of modeling the ecosystem as a basic model system and reproduced it in real time using a computer and simulator. Therefore, this is different from the chaos theory, which is static and solved in a stationary state. Fortunately, the new solution does not overlap or conflict with the existing logical solution (chaos theory); therefore, we will have to use both solutions.\u003c/p\u003e","manuscriptTitle":"Complex Systems Must Be Solved with Systematic Solution; How can We Solve Systematic Problem Such as Ecosystems Using Systematic Solution Dynamically","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-31 09:02:30","doi":"10.21203/rs.3.rs-6101727/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ddfa0766-c665-4c78-9eb3-a197c99c0586","owner":[],"postedDate":"March 31st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-07-07T07:55:09+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-31 09:02:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6101727","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6101727","identity":"rs-6101727","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}