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

页数：15

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