Bifurcation Analysis for a Class of Cubic Switching Systems

被引：1

作者：

Wang, Xiangyu ^{[1
]}

Wu, Yusen ^{[2
]}

Guo, Laigang ^{[3
]}

机构：

[1] Beihang Univ, Sch Math Sci, Beijing 100191, Peoples R China

[2] Qufu Normal Univ, Sch Stat, Qufu 273165, Shandong, Peoples R China

[3] Beijing Normal Univ, Sch Math Sci, Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2022年 / 32卷 / 05期

基金：

中国国家自然科学基金;

关键词：

Switching system; Lyapunov constant; center; limit cycle; Poincare return map; LIMIT-CYCLES; HOPF BIFURCATIONS; PLANAR; CENTERS;

D O I：

10.1142/S0218127422500730

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider a class of switching systems perturbed by cubic homogeneous polynomials. This class of systems is separated by a straight line: y = 0, and has three equilibria: (0, 0) and (+/- 1, 0) which are in the separation line. A new version of the Gasull-Torregrosa method based on Poincare return maps is presented, and used to compute the Lyapunov constants. Based on this method, a complete classification on the center conditions is obtained for the studied class of systems. Furthermore, by perturbing the cubic switching integral system with cubic homogeneous polynomials, we show that at least ten small-amplitude limit cycles are obtained around one of the centres. This is a new lower bound for the number of limit cycles bifurcating from a center in such switching systems with cubic homogeneous nonlinearities.

引用

页数：19

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