Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems

被引：0
|
作者：
Hua, Duo [1 ,2 ]
Liu, Xingbo [1 ,2 ]
机构：
[1] East China Normal Univ, Sch Math Sci, Key Lab MEA, Minist Educ, Shanghai 200241, Peoples R China
[2] East China Normal Univ, Shanghai Key Lab PMMP, Shanghai 200241, Peoples R China
来源：
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2024年
基金：
中国国家自然科学基金;
关键词：
Discontinuous systems; Homoclinic cycle; Limit cycle; Lin's method; MELNIKOV METHOD; LINS METHOD; ORBITS; EQUILIBRIUM;
D O I：
10.1007/s10884-024-10358-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页数：26
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