Slowly Oscillating Periodic Solutions of a Van der Pol Oscillator with State-Dependent Delay

Slowly Oscillating Periodic Solutions of a Van der Pol Oscillator with State-Dependent Delay | 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 Slowly Oscillating Periodic Solutions of a Van der Pol Oscillator with State-Dependent Delay Aiyu Hou, shunlian Liu, Chaoliang Luo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4784921/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 In this paper, we consider a Van der Pol oscillator with state-dependent delay. Firstly, we seek for a suitable set $E$ on which we construct a Poincar'e operator $F$. Then, we prove that the operator $F$ is continuous and compact on $E\backslash{0}$. After that, we obtain the ejectivity of the trivial fixed point ${0}$ and the existence of slowly oscillating periodic solution. Finally, we choose an example of state-dependent delay to test our analytical result by comparing it to numerical continuation.This theoretical result generalizes and improves some existing results. Van der Pol oscillator slowly oscillating periodic solutions state- dependent delay 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. 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