Limit cycles for discontinuous planar piecewise linear differential systems separated by one straight line and having a center

被引：45

作者：

Llibre, Jaume ^{[1
]}

Zhang, Xiang ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain

[2] Shanghai Jiao Tong Univ, Minist Educ, Key Lab Sci & Engn Comp, Sch Math Sci, Shanghai 200240, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 467卷 / 01期

关键词：

Non-smooth differential system; Limit cycle; Discontinuous piecewise linear differential system; BIFURCATIONS; NUMBER;

D O I：

10.1016/j.jmaa.2018.07.024

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

From the beginning of this century more than thirty papers have been published studying the limit cycles of the discontinuous piecewise linear differential systems with two pieces separated by a straight line, but it remains open the following question: what is the maximum number of limit cycles that this class of differential systems can have? Here we prove that when one of the linear differential systems has a center, real or virtual, then the discontinuous piecewise linear differential system has at most two limit cycles. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：537 / 549

页数：13

共 50 条

[21] The Markus-Yamabe Conjecture Does not Hold for Discontinuous Piecewise Linear Differential Systems Separated by One Straight Line
Llibre, Jaume
Menezes, Lucyjane de A. S.
JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2021, 33 (02) : 659 - 676
[22] Limit cycles of discontinuous piecewise differential systems formed by two rigid systems separated by a straight lineLimit cycles of discontinuous piecewise differential systemsJ. Llibre et al.
Jaume Llibre
Angela C. T. Sánchez
Durval J. Tonon
Nonlinear Differential Equations and Applications NoDEA, 2025, 32 (3)
[23] Limit Cycles in the Discontinuous Planar Piecewise Linear Systems with Three Zones
Li, Zhengkang
Liu, Xingbo
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2021, 20 (03)
[24] Limit Cycles in the Discontinuous Planar Piecewise Linear Systems with Three Zones
Zhengkang Li
Xingbo Liu
Qualitative Theory of Dynamical Systems, 2021, 20
[25] Algebraic limit cycles of planar discontinuous piecewise linear differential systems with an angular switching boundary
Llibre, Jaume
Xiong, Haichao
Zhang, Weinian
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2025, 546 (02)
[26] ARBITRARY NUMBER OF LIMIT CYCLES FOR PLANAR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH TWO ZONES
Braga, Denis De Carvalho
Mello, Luis Fernando
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2015,
[27] Limit cycles bifurcating from piecewise quadratic systems separated by a straight line
Peng, Linping
Gao, Yunfei
Feng, Zhaosheng
Nonlinear Analysis, Theory, Methods and Applications, 2020, 196
[28] Limit cycles bifurcating from piecewise quadratic systems separated by a straight line
Peng, Linping
Gao, Yunfei
Feng, Zhaosheng
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 196
[29] LIMIT CYCLES OF CONTINUOUS PIECEWISE DIFFERENTIAL SYSTEMS SEPARATED BY A PARABOLA AND FORMED BY A LINEAR CENTER AND A QUADRATIC CENTER
Llibre, Jaume
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2023, 16 (3-4): : 533 - 547
[30] Limit Cycles in a Family of Planar Piecewise Linear Differential Systems with a Nonregular Separation Line
Huan, Song-Mei
Yang, Xiao-Song
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2019, 29 (08):

← 1 2 3 4 5 →