Circuit simulation experiment verification of the integrability of three kinds of nonlinear dynamical systems

Circuit simulation experiment verification of the integrability of three kinds of nonlinear dynamical systems | 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 Circuit simulation experiment verification of the integrability of three kinds of nonlinear dynamical systems Yuhan Song, Chang Liu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7495025/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 Up to now, most research papers of integrability of differential equations are emphasized on theoretical proof. However, there is no work about experimental verification of integrability. To solve the problem, this paper we focus on circuit simulation experiment of the integrability of nonlinear dynamical systems. The integrability of nonlinear dynamical systems is investigated by circuit simulation experiment. The integrability conditions for three kinds of nonlinear systems are reviewed. Then, the circuit diagrams corresponding to the nonlinear systems are designed by using Kirchhoff’s law, the circuit models are established via the Multisim 14.0 simulation software. The realization of the integrable nonlinear systems in the circuit is examined, and the results of the analytical solutions of the equations are compared with the simulation results of the circuit, the circuit simulation experiment indicates that the simulation results support the analytical solutions. It is further proved that the integrability of nonlinear systems is effective. Nonlinear system Integrability Circuit realization Multisim simulation Full Text Additional Declarations No competing interests reported. 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-7495025","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":524674579,"identity":"2fa942b3-298d-4e22-8f40-0fa69a549f40","order_by":0,"name":"Yuhan Song","email":"","orcid":"","institution":"Liaoning University","correspondingAuthor":false,"prefix":"","firstName":"Yuhan","middleName":"","lastName":"Song","suffix":""},{"id":524674580,"identity":"3c35db22-2821-465a-8966-2525bba48f6f","order_by":1,"name":"Chang Liu","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0UlEQVRIiWNgGAWjYDACCRBRIMHAzw7mMhOrxUCCQbKZRC1AdJhYLfyzm589/GJgkbj5MO8xCYYK68QG9rMH8Fty55i5sYyBROK2w3xpEgxn0hMbePIS8GoxkEgwk5YAa+Exk2BsO5zYIMFjQEBL+jewls3NIC3/iNKSYyb5AahlAzNISwMRWiRu5JRJAzUazzjMY2yRcCzduI0nB78W/hnp2yR/VNTJ9rf3GN74UGMt289+Br8WEGDmgbESgJiNoHogYPxBjKpRMApGwSgYuQAAIyM6wuiBI0sAAAAASUVORK5CYII=","orcid":"","institution":"Liaoning University","correspondingAuthor":true,"prefix":"","firstName":"Chang","middleName":"","lastName":"Liu","suffix":""}],"badges":[],"createdAt":"2025-08-30 11:38:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7495025/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7495025/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":92911825,"identity":"19e0db26-34fc-4ac8-86e4-e6de374720c5","added_by":"auto","created_at":"2025-10-07 04:05:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1248392,"visible":true,"origin":"","legend":"","description":"","filename":"Liuarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7495025/v1/6c3c14fb12dfb5deb229e590.pdf"},{"id":92911824,"identity":"5c22d415-2d20-4c31-895e-d3f1c0abd017","added_by":"auto","created_at":"2025-10-07 04:05:15","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3687,"visible":true,"origin":"","legend":"","description":"","filename":"430b51e76332485fa2d211416b52bfe5.json","url":"https://assets-eu.researchsquare.com/files/rs-7495025/v1/35954a65130e302ef317c8e8.json"},{"id":98625528,"identity":"0f151601-001f-4a7b-86f5-9d2d2a307711","added_by":"auto","created_at":"2025-12-19 17:09:10","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1018938,"visible":true,"origin":"","legend":"","description":"","filename":"Liuarticle.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7495025/v1_covered_c556af50-759c-449a-9db8-c3343c4b8834.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Circuit simulation experiment verification of the integrability of three kinds of nonlinear dynamical systems","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"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":"Nonlinear system, Integrability, Circuit realization, Multisim simulation","lastPublishedDoi":"10.21203/rs.3.rs-7495025/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7495025/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"Up to now, most research papers of integrability of differential equations are emphasized on theoretical proof. 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