Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems

Duo Hua; Xingbo Liu

doi:10.1007/s10884-024-10358-7

Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems

Duo Hua
, Xingbo Liu^*

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	2513-2538
Number of pages	26
Journal	Journal of Dynamics and Differential Equations
Volume	37
Issue number	3
DOIs	https://doi.org/10.1007/s10884-024-10358-7
State	Published - Sep 2025

Keywords

Discontinuous systems
Homoclinic cycle
Limit cycle
Lin’s method

Access to Document

10.1007/s10884-024-10358-7

Cite this

@article{3ac7f0d179bc465f86cb505e60b05ef6,

title = "Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems",

abstract = "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{\textquoteright}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.",

keywords = "Discontinuous systems, Homoclinic cycle, Limit cycle, Lin{\textquoteright}s method",

author = "Duo Hua and Xingbo Liu",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.",

year = "2025",

month = sep,

doi = "10.1007/s10884-024-10358-7",

language = "英语",

volume = "37",

pages = "2513--2538",

journal = "Journal of Dynamics and Differential Equations",

issn = "1040-7294",

publisher = "Springer",

number = "3",

}

TY - JOUR

T1 - Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems

AU - Hua, Duo

AU - Liu, Xingbo

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.

PY - 2025/9

Y1 - 2025/9

N2 - 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.

AB - 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.

KW - Discontinuous systems

KW - Homoclinic cycle

KW - Limit cycle

KW - Lin’s method

UR - https://www.scopus.com/pages/publications/85188555502

U2 - 10.1007/s10884-024-10358-7

DO - 10.1007/s10884-024-10358-7

M3 - 文章

AN - SCOPUS:85188555502

SN - 1040-7294

VL - 37

SP - 2513

EP - 2538

JO - Journal of Dynamics and Differential Equations

JF - Journal of Dynamics and Differential Equations

IS - 3

ER -

Limit Cycle Bifurcations Near Nonsmooth Homoclinic Cycle in Discontinuous Systems

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this