Limit Cycles of a Planar Piecewise Linear System with an Improper Node

被引:0
|
作者
Xiao, Ning [1 ]
Wu, Kuilin [1 ]
机构
[1] Guizhou Univ, Sch Math & Stat, Guiyang 550025, Peoples R China
来源
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2023年 / 33卷 / 15期
关键词
Limit cycle; piecewise linear system; improper node; DIFFERENTIAL-EQUATIONS; REFRACTING SYSTEMS; PHASE PORTRAITS; EXISTENCE; NUMBER;
D O I
10.1142/S021812742350178X
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
This paper is concerned with the number of limit cycles for a planar piecewise linear (PWL) system with two zones separated by a straight line. Assume that one of the subsystems of the PWL system has an improper node. The number of limit cycles for saddle-improper node type, focus-improper node type and center-improper node type (the focus or the center is a virtual or boundary equilibrium) are studied. First, we introduce displacement functions and study the number of zeros of displacement functions for different types. Then, we give the parameter regions where the exact number of limit cycles is one or two (at least two) for different types.
引用
收藏
页数:15
相关论文
共 50 条
  • [1] LIMIT CYCLES FOR PIECEWISE LINEAR SYSTEMS WITH IMPROPER NODE
    Zhao, Hefei
    Wu, Kuilin
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2023, 13 (05): : 2720 - 2738
  • [2] SADDLE-NODE OF LIMIT CYCLES IN PLANAR PIECEWISE LINEAR SYSTEMS AND APPLICATIONS
    Carmona, Victoriano
    Fernandez-garcia, Soledad
    Teruel, Antonio E.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2019, 39 (09) : 5275 - 5299
  • [3] On the number of limit cycles in general planar piecewise linear systems of node-node types
    Huan, Song-Mei
    Yang, Xiao-Song
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 411 (01) : 340 - 353
  • [4] Limit cycles in planar continuous piecewise linear systems
    Chen, Hebai
    Li, Denghui
    Xie, Jianhua
    Yue, Yuan
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 47 : 438 - 454
  • [5] The number and stability of limit cycles for planar piecewise linear systems of node-saddle type
    Wang, Jiafu
    Chen, Xiaoyan
    Huang, Lihong
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 469 (01) : 405 - 427
  • [6] Impact limit cycles in the planar piecewise linear hybrid systems
    Li, Zhengkang
    Liu, Xingbo
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2023, 119
  • [7] Uniqueness of limit cycles for sewing planar piecewise linear systems
    Medrado, Joao C.
    Torregrosa, Joan
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 431 (01) : 529 - 544
  • [8] ON THE NUMBER OF LIMIT CYCLES IN GENERAL PLANAR PIECEWISE LINEAR SYSTEMS
    Huan, Song-Mei
    Yang, Xiao-Song
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2012, 32 (06) : 2147 - 2164
  • [9] Limit Cycles of Planar Piecewise Differential Systems with Linear Hamiltonian Saddles
    Llibre, Jaume
    Valls, Claudia
    SYMMETRY-BASEL, 2021, 13 (07):
  • [10] Limit cycles from a monodromic infinity in planar piecewise linear systems
    Freire, Emilio
    Ponce, Enrique
    Torregrosa, Joan
    Torres, Francisco
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 496 (02)