Investigation of Novel Modified ABC Differential Operator in Chaotic System Application with Deep Neural Networks

Investigation of Novel Modified ABC Differential Operator in Chaotic System Application with Deep Neural Networks | 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 Investigation of Novel Modified ABC Differential Operator in Chaotic System Application with Deep Neural Networks Atul Kumar This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6845816/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 The main focus of the inquiry is the Newton-Leipnik system in piecewise approach. Piecewise differential and integral operator theory, as well as its applications, have grown significantly. By assessing the state of the art and approaching the subject in a methodical manner, this essay aims to provide an outcome for this circumstance. We might observe an attractor in this system. Using piecewise modelling, this system illustrates Newton-Leipnik's method. The piecewise derivatives are introduced in this study together with the Newton-Leipnik system. It is possible to approximate these piecewise derivatives using the Adams-Bashforth approach. Using detailed numerical simulations, the numerical results have been confirmed and demonstrated. Our investigation focusses on the piecewise Newton-Leipnik system with two strange attractors and its chaotic dynamics. The Newton-Leipnik system behaves in real life with piecewise patterns shown in the numerical simulations. Systems and Networking Computational Mathematics Applied Mathematics Modified ABC Differential Operator Modified Newton Leipnik systems Nonlinear Equations Piecewise Models Chaos and Cross-over Behaviors Full Text Additional Declarations The authors declare no competing interests. Supplementary Files LeipnikMABC.tex 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-6845816","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":468073388,"identity":"7f5fd663-6d11-4bee-a38a-cb04a15c165d","order_by":0,"name":"Atul Kumar","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA8klEQVRIiWNgGAWjYHACxgMJFTU8bOztBx8AeTx8BDWwMTAceHDmmBwfz5lkA5AWNmK0HHzYxmwsJ5FgJgEVwA/45/cYHEhgY0tsY0hIq/yaYyfDxsD88NENPFokjvEAtfDIALUcPHZbdlsy0GFsxsY5+KwBa5EA2sLYkHZbchszUAsPmzQ+LfJgLQbMiW3MDGbFktvqCWsxAGtJYDZmY2MwY/y47TBhLYbH0goOJBw4JsfGw5MszbjtOA8bMwG/yB0+vPHhz381PPLznx/8+HNbtT0/e/PDx3i9jwyYecAkscpBgPEHKapHwSgYBaNgxAAAWgVHDTYpIwsAAAAASUVORK5CYII=","orcid":"https://orcid.org/0009-0000-3313-7829","institution":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, SIMATS, Chennai, India","correspondingAuthor":true,"prefix":"","firstName":"Atul","middleName":"","lastName":"Kumar","suffix":""}],"badges":[],"createdAt":"2025-06-08 06:28:05","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-6845816/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6845816/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":84292057,"identity":"8bb36e3f-55fb-41f4-98d6-ee9ce9a109fd","added_by":"auto","created_at":"2025-06-10 08:52:49","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":8771147,"visible":true,"origin":"","legend":"","description":"","filename":"LeipnikMABC.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6845816/v1_covered_21a4a5c8-f612-4279-92bf-39896e3c02c2.pdf"},{"id":84291276,"identity":"ffbbc6b7-b667-4f3e-bfca-7d08cf32a192","added_by":"auto","created_at":"2025-06-10 08:44:41","extension":"tex","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":40054,"visible":true,"origin":"","legend":"","description":"","filename":"LeipnikMABC.tex","url":"https://assets-eu.researchsquare.com/files/rs-6845816/v1/7b10fd0d339c3e121b80eece.tex"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eInvestigation of Novel Modified ABC Differential Operator in Chaotic System Application with Deep Neural Networks\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, SIMATS, Chennai, India","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"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":" Modified ABC Differential Operator, Modified Newton Leipnik systems, Nonlinear Equations, Piecewise Models, Chaos and Cross-over Behaviors","lastPublishedDoi":"10.21203/rs.3.rs-6845816/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6845816/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\t\tThe main focus of the inquiry is the Newton-Leipnik system in piecewise approach. Piecewise differential and integral operator theory, as well as its applications, have grown significantly. By assessing the state of the art and approaching the subject in a methodical manner, this essay aims to provide an outcome for this circumstance. We might observe an attractor in this system. Using piecewise modelling, this system illustrates Newton-Leipnik's method. The piecewise derivatives are introduced in this study together with the Newton-Leipnik system. It is possible to approximate these piecewise derivatives using the Adams-Bashforth approach. Using detailed numerical simulations, the numerical results have been confirmed and demonstrated. Our investigation focusses on the piecewise Newton-Leipnik system with two strange attractors and its chaotic dynamics. The Newton-Leipnik system behaves in real life with piecewise patterns shown in the numerical simulations.\u003c/p\u003e","manuscriptTitle":"Investigation of Novel Modified ABC Differential Operator in Chaotic System Application with Deep Neural Networks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-06-10 08:44:36","doi":"10.21203/rs.3.rs-6845816/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":"da3365f8-4759-422f-982c-4d245844e181","owner":[],"postedDate":"June 10th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":49696119,"name":"Systems and Networking"},{"id":49696120,"name":"Computational Mathematics"},{"id":49696121,"name":"Applied Mathematics"}],"tags":[],"updatedAt":"2025-06-10T08:44:36+00:00","versionOfRecord":[],"versionCreatedAt":"2025-06-10 08:44:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6845816","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6845816","identity":"rs-6845816","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}