{"title":"有两个不恰当节点的不连续平面片断线性系统最多有一个极限周期","authors":"Lu Chen, Changjian Liu","doi":"10.1016/j.nonrwa.2024.104180","DOIUrl":null,"url":null,"abstract":"<div><p>The existence and number of limit cycles of planar piecewise linear systems with two improper nodes are studied. By constructing the Poincaré half maps and the successor function, we prove that such systems have at most one limit cycle, and when the limit cycle exists, it must be hyperbolic. Furthermore, we explicitly give the parameter regions where the limit cycle exists.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"80 ","pages":"Article 104180"},"PeriodicalIF":1.8000,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The discontinuous planar piecewise linear systems with two improper nodes have at most one limit cycle\",\"authors\":\"Lu Chen, Changjian Liu\",\"doi\":\"10.1016/j.nonrwa.2024.104180\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The existence and number of limit cycles of planar piecewise linear systems with two improper nodes are studied. By constructing the Poincaré half maps and the successor function, we prove that such systems have at most one limit cycle, and when the limit cycle exists, it must be hyperbolic. Furthermore, we explicitly give the parameter regions where the limit cycle exists.</p></div>\",\"PeriodicalId\":49745,\"journal\":{\"name\":\"Nonlinear Analysis-Real World Applications\",\"volume\":\"80 \",\"pages\":\"Article 104180\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Real World Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001202\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2024/7/18 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001202","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/7/18 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
The discontinuous planar piecewise linear systems with two improper nodes have at most one limit cycle
The existence and number of limit cycles of planar piecewise linear systems with two improper nodes are studied. By constructing the Poincaré half maps and the successor function, we prove that such systems have at most one limit cycle, and when the limit cycle exists, it must be hyperbolic. Furthermore, we explicitly give the parameter regions where the limit cycle exists.
期刊介绍：
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
