{"title":"正则化片断线性可见-不可见二折线的滑动循环","authors":"Renato Huzak, Kristian Uldall Kristiansen","doi":"10.1007/s12346-024-01111-y","DOIUrl":null,"url":null,"abstract":"<p>The goal of this paper is to study the number of sliding limit cycles of regularized piecewise linear visible–invisible twofolds using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the half-plane with an invisible fold point. We prove that the integral has at most 1 zero counting multiplicity (when it is not identically zero). This will imply that the canard cycles can produce at most 2 limit cycles. Moreover, we detect regions in the parameter space with 2 limit cycles.</p>","PeriodicalId":48886,"journal":{"name":"Qualitative Theory of Dynamical Systems","volume":"45 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds\",\"authors\":\"Renato Huzak, Kristian Uldall Kristiansen\",\"doi\":\"10.1007/s12346-024-01111-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The goal of this paper is to study the number of sliding limit cycles of regularized piecewise linear visible–invisible twofolds using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the half-plane with an invisible fold point. We prove that the integral has at most 1 zero counting multiplicity (when it is not identically zero). This will imply that the canard cycles can produce at most 2 limit cycles. Moreover, we detect regions in the parameter space with 2 limit cycles.</p>\",\"PeriodicalId\":48886,\"journal\":{\"name\":\"Qualitative Theory of Dynamical Systems\",\"volume\":\"45 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-08-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Qualitative Theory of Dynamical Systems\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s12346-024-01111-y\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Qualitative Theory of Dynamical Systems","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s12346-024-01111-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Sliding Cycles of Regularized Piecewise Linear Visible–Invisible Twofolds
The goal of this paper is to study the number of sliding limit cycles of regularized piecewise linear visible–invisible twofolds using the notion of slow divergence integral. We focus on limit cycles produced by canard cycles located in the half-plane with an invisible fold point. We prove that the integral has at most 1 zero counting multiplicity (when it is not identically zero). This will imply that the canard cycles can produce at most 2 limit cycles. Moreover, we detect regions in the parameter space with 2 limit cycles.
期刊介绍:
Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.