A K–R Parameterized Nonlinear Wetware Framework with Global Lyapunov Stability and Quantitative Convergence Benchmarks

A K–R Parameterized Nonlinear Wetware Framework with Global Lyapunov Stability and Quantitative Convergence Benchmarks | 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 A K–R Parameterized Nonlinear Wetware Framework with Global Lyapunov Stability and Quantitative Convergence Benchmarks RamaKrishna Pasupuleti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8715671/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 We propose a nonlinear wetware-inspired dynamical framework governed by a two-parameter K–R structure, where the excitation parameter \(\:K\:\) and the regulation parameter \(\:R\:\) provide interpretable control over system plasticity and stabilization. The model incorporates biologically motivated saturation nonlinearities and is analyzed using a non-quadratic Lyapunov function specifically tailored to the system dynamics. Rigorous analysis establishes global asymptotic stability of the equilibrium for all admissible initial conditions and parameter ranges. To validate the theoretical results, extensive numerical simulations are conducted. State trajectory analyses demonstrate robust global convergence from widely separated initial conditions under variations of \(\:K\) , \(\:R\) , and nonlinear gain parameters. The Lyapunov function is shown to decay monotonically along all simulated trajectories, providing strong numerical confirmation of the analytical stability guarantees. Phase-portrait analysis further illustrates how excitation gain reshapes the vector field while preserving global stability and a unique equilibrium. Beyond qualitative validation, a quantitative convergence benchmark is introduced through settling-time analysis. Numerical experiments reveal a clear dependence of convergence speed on the excitation–regulation trade-off, showing that the K–R framework enables explicit and measurable control of stabilization dynamics. In particular, increasing excitation strength accelerates convergence after an initial regime, highlighting a nontrivial performance–stability interaction induced by nonlinear saturation. Overall, the results demonstrate that the proposed K–R framework unifies global Lyapunov stability, nonlinear wetware modeling, and quantitative convergence characterization within a single, interpretable dynamical system. This combination provides a mathematically rigorous and computationally reproducible foundation for analyzing stability–plasticity trade-offs in nonlinear neural and wetware-inspired systems. Full Text Additional Declarations No competing interests reported. Supplementary Files wetwareKRlyapunov.py 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-8715671","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":585296765,"identity":"25b747b0-e871-4044-ac0c-2e68c11a6cc9","order_by":0,"name":"RamaKrishna Pasupuleti","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9ElEQVRIiWNgGAWjYHACZoYEBjkgfbD9wwcgxcZOnBZjBgbGw22MM0BamInRwgDSwny8jZkHxscHDI73PjZ48McgcTvbwbbHNr+2yfMxMzB++JiDR8uZ48YJiW0GiTt7DrYb5/bdNmxjZmCWnLkNtxazG2nMBxIb/iRuuHGwQTq35zYjUAsbMy8hLQlAh224/7BB2rLntj1RWhIS2IBaDhxsk2b4cTuRoBb7M8eYDYB+MQZqaTbsbbid3MbM2IzXL5LtbcySP/4YyG44cPzhgx9/btvOb28++OEjHi2ogLENTDYQqx4E/pCieBSMglEwCkYKAAAdgVk9CekE7wAAAABJRU5ErkJggg==","orcid":"","institution":"Kakatiya University","correspondingAuthor":true,"prefix":"","firstName":"RamaKrishna","middleName":"","lastName":"Pasupuleti","suffix":""}],"badges":[],"createdAt":"2026-01-28 03:09:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8715671/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8715671/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101943438,"identity":"88103d45-eabe-4c57-a77d-dd4a8b72a046","added_by":"auto","created_at":"2026-02-05 09:41:57","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":592682,"visible":true,"origin":"","legend":"","description":"","filename":"NonlinearWetwareFrameworkwithGlobalLyapunovStability.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8715671/v1_covered_d946c13c-0f36-40bb-910a-ca2036537ea6.pdf"},{"id":101926002,"identity":"6d4a0a81-60eb-426a-8a74-19d6a4f226fd","added_by":"auto","created_at":"2026-02-05 06:16:44","extension":"py","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":2591,"visible":true,"origin":"","legend":"","description":"","filename":"wetwareKRlyapunov.py","url":"https://assets-eu.researchsquare.com/files/rs-8715671/v1/ce70aa9215fb823ace977524.py"}],"financialInterests":"No competing interests reported.","formattedTitle":"A K–R Parameterized Nonlinear Wetware Framework with Global Lyapunov Stability and Quantitative Convergence Benchmarks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"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":"","lastPublishedDoi":"10.21203/rs.3.rs-8715671/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8715671/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe propose a nonlinear wetware-inspired dynamical framework governed by a two-parameter K\u0026ndash;R structure, where the excitation parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:K\\:\\)\u003c/span\u003e\u003c/span\u003eand the regulation parameter \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\:\\)\u003c/span\u003e\u003c/span\u003eprovide interpretable control over system plasticity and stabilization. The model incorporates biologically motivated saturation nonlinearities and is analyzed using a non-quadratic Lyapunov function specifically tailored to the system dynamics. Rigorous analysis establishes \u003cb\u003eglobal asymptotic stability\u003c/b\u003e of the equilibrium for all admissible initial conditions and parameter ranges.\u003c/p\u003e \u003cp\u003eTo validate the theoretical results, extensive numerical simulations are conducted. State trajectory analyses demonstrate robust global convergence from widely separated initial conditions under variations of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:K\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e\u003c/span\u003e, and nonlinear gain parameters. The Lyapunov function is shown to decay monotonically along all simulated trajectories, providing strong numerical confirmation of the analytical stability guarantees. Phase-portrait analysis further illustrates how excitation gain reshapes the vector field while preserving global stability and a unique equilibrium.\u003c/p\u003e \u003cp\u003eBeyond qualitative validation, a \u003cb\u003equantitative convergence benchmark\u003c/b\u003e is introduced through settling-time analysis. Numerical experiments reveal a clear dependence of convergence speed on the excitation\u0026ndash;regulation trade-off, showing that the K\u0026ndash;R framework enables explicit and measurable control of stabilization dynamics. In particular, increasing excitation strength accelerates convergence after an initial regime, highlighting a nontrivial performance\u0026ndash;stability interaction induced by nonlinear saturation.\u003c/p\u003e \u003cp\u003eOverall, the results demonstrate that the proposed K\u0026ndash;R framework unifies \u003cb\u003eglobal Lyapunov stability, nonlinear wetware modeling, and quantitative convergence characterization\u003c/b\u003e within a single, interpretable dynamical system. This combination provides a mathematically rigorous and computationally reproducible foundation for analyzing stability\u0026ndash;plasticity trade-offs in nonlinear neural and wetware-inspired systems.\u003c/p\u003e","manuscriptTitle":"A K–R Parameterized Nonlinear Wetware Framework with Global Lyapunov Stability and Quantitative Convergence Benchmarks","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-02-05 06:16:38","doi":"10.21203/rs.3.rs-8715671/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":"dafb1023-9678-48dc-92fe-bcfd0983ee2d","owner":[],"postedDate":"February 5th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-02-05T06:16:39+00:00","versionOfRecord":[],"versionCreatedAt":"2026-02-05 06:16:38","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8715671","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8715671","identity":"rs-8715671","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}