{"title":"带三个区的连续平面片断线性微分系统的全局分析","authors":"Man Jia, Youfeng Su, Hebai Chen","doi":"10.58997/ejde.2023.83","DOIUrl":null,"url":null,"abstract":"This article concerns the global dynamics of a continuous planar piecewise linear differential system with three zones. We give global phase portraits in the Poincare disc and classify bifurcation diagrams under certain parametric conditions, when the dynamics of central linear zone is anti-saddle. Rich dynamical behaviors are demonstrated, from which we observe homoclinic loops appearing in three linear zones and limit cycles occurring in three linear zones which surround a node or node-focus. \nFor more information see https://ejde.math.txstate.edu/Volumes/2023/83/abstr.html","PeriodicalId":49213,"journal":{"name":"Electronic Journal of Differential Equations","volume":"991 ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global analysis on a continuous planar piecewise linear differential system with three zones\",\"authors\":\"Man Jia, Youfeng Su, Hebai Chen\",\"doi\":\"10.58997/ejde.2023.83\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This article concerns the global dynamics of a continuous planar piecewise linear differential system with three zones. We give global phase portraits in the Poincare disc and classify bifurcation diagrams under certain parametric conditions, when the dynamics of central linear zone is anti-saddle. Rich dynamical behaviors are demonstrated, from which we observe homoclinic loops appearing in three linear zones and limit cycles occurring in three linear zones which surround a node or node-focus. \\nFor more information see https://ejde.math.txstate.edu/Volumes/2023/83/abstr.html\",\"PeriodicalId\":49213,\"journal\":{\"name\":\"Electronic Journal of Differential Equations\",\"volume\":\"991 \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-12-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.58997/ejde.2023.83\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.58997/ejde.2023.83","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Global analysis on a continuous planar piecewise linear differential system with three zones
This article concerns the global dynamics of a continuous planar piecewise linear differential system with three zones. We give global phase portraits in the Poincare disc and classify bifurcation diagrams under certain parametric conditions, when the dynamics of central linear zone is anti-saddle. Rich dynamical behaviors are demonstrated, from which we observe homoclinic loops appearing in three linear zones and limit cycles occurring in three linear zones which surround a node or node-focus.
For more information see https://ejde.math.txstate.edu/Volumes/2023/83/abstr.html
期刊介绍:
All topics on differential equations and their applications (ODEs, PDEs, integral equations, delay equations, functional differential equations, etc.) will be considered for publication in Electronic Journal of Differential Equations.