{"title":"非连续系统中接近非光滑同线性周期的极限周期分岔","authors":"Duo Hua, Xingbo Liu","doi":"10.1007/s10884-024-10358-7","DOIUrl":null,"url":null,"abstract":"<p>The main aim of this paper is to study the limit cycle bifurcations near the homoclinic cycle in the discontinuous systems. Based on the impoved Lin’s method, we establish the bifurcation equation, which presents the existence of limit cycles bifurcated from nonsmooth homoclinic cycles under perturbation. Furthermore, we give an example to support our conclusions. After solving a boundary value problem with numerical tools, we provide the exact parameter values for the system having a limit cycle.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"12 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems\",\"authors\":\"Duo Hua, Xingbo Liu\",\"doi\":\"10.1007/s10884-024-10358-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The main aim of this paper is to study the limit cycle bifurcations near the homoclinic cycle in the discontinuous systems. Based on the impoved Lin’s method, we establish the bifurcation equation, which presents the existence of limit cycles bifurcated from nonsmooth homoclinic cycles under perturbation. Furthermore, we give an example to support our conclusions. After solving a boundary value problem with numerical tools, we provide the exact parameter values for the system having a limit cycle.</p>\",\"PeriodicalId\":15624,\"journal\":{\"name\":\"Journal of Dynamics and Differential Equations\",\"volume\":\"12 1\",\"pages\":\"\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-03-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10884-024-10358-7\",\"RegionNum\":4,\"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":"Journal of Dynamics and Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10884-024-10358-7","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems
The main aim of this paper is to study the limit cycle bifurcations near the homoclinic cycle in the discontinuous systems. Based on the impoved Lin’s method, we establish the bifurcation equation, which presents the existence of limit cycles bifurcated from nonsmooth homoclinic cycles under perturbation. Furthermore, we give an example to support our conclusions. After solving a boundary value problem with numerical tools, we provide the exact parameter values for the system having a limit cycle.
期刊介绍：
Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.
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