Limit Cycles from Perturbing a Piecewise Smooth System with a Center and a Homoclinic Loop

被引：0
|
作者：
Ke, Ai [1 ]
Han, Maoan [2 ]
机构：
[1] Shanghai Normal Univ, Dept Math, Shanghai 200234, Peoples R China
[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
来源：
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2021年 / 31卷 / 10期
关键词：
Limit cycle; bifurcation; isochronous center; Melnikov function; PERIODIC-SOLUTIONS; BIFURCATIONS; NUMBER; HOPF;
D O I：
10.1142/S0218127421501595
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study bifurcations of limit cycles arising after perturbations of a special piecewise smooth system, which has a center and a homoclinic loop. By using the Picard-Fuchs equation, we give an upper bound of the maximum number of limit cycles bifurcated from the period annulus between the center and the homoclinic loop. Furthermore, by applying the method of first-order Melnikov function we obtain a lower bound of the maximum number of limit cycles bifurcated from the center.
引用
收藏
页数：15
相关论文
共 50 条
  • [21] LIMIT CYCLE BIFURCATIONS BY PERTURBING A KIND OF QUADRATIC HAMILTONIAN SYSTEM HAVING A HOMOCLINIC LOOP
    Xiong, Yanqin
    Zhao, Liqin
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2024, 29 (11): : 4416 - 4431
  • [22] On the maximum number of limit cycles for a piecewise smooth differential system
    Shi, Hongwei
    Bai, Yuzhen
    Han, Maoan
    BULLETIN DES SCIENCES MATHEMATIQUES, 2020, 163
  • [23] Limit cycle bifurcations in a class of piecewise smooth systems with a double homoclinic loop
    Liu, Yuanyuan
    Romanovski, Valery G.
    APPLIED MATHEMATICS AND COMPUTATION, 2014, 248 : 235 - 245
  • [24] Limit Cycles Appearing From Piecewise Smooth Perturbations to a Reversible Nonlinear Center
    Sun, Dan
    Peng, Linping
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2021, 31 (16):
  • [25] On the Number of Limit Cycles Bifurcated from Some Hamiltonian Systems with a Double Homoclinic Loop and a Heteroclinic Loop
    Moghimi, Pegah
    Asheghi, Rasoul
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2017, 27 (04):
  • [26] Bifurcation of Limit Cycles of a Piecewise Smooth Hamiltonian System
    Jihua Yang
    Liqin Zhao
    Qualitative Theory of Dynamical Systems, 2022, 21
  • [27] Bifurcation of limit cycles in a piecewise smooth near-integrable system
    Tian, Yun
    Shang, Xinyu
    Han, Maoan
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 504 (02)
  • [28] Limit Cycles for a Class of Piecewise Smooth Quadratic Differential Systems with Multiple Parameters
    Bo, Xuekang
    Tian, Yun
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2016, 26 (10):
  • [29] On the Number of Limit Cycles in Small Perturbations of a Piecewise Linear Hamiltonian System with a Heteroclinic Loop
    Liang, Feng
    Han, Maoan
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2016, 37 (02) : 267 - 280
  • [30] Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth systems with a cusp
    Wei, Lijun
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2017, 38 : 306 - 326
12345