Center conditions in a switching Bautin system

被引：47

作者：

Tian, Yun ^{[1
]}

Yu, Pei ^{[1
]}

机构：

[1] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Switching system; Bautin switching system; Lyapunov constant; Center; Bifurcation; Limit cycle; HOPF-BIFURCATION; LIMIT-CYCLES; PIECEWISE-SMOOTH; LIENARD SYSTEMS; PLANAR;

D O I：

10.1016/j.jde.2015.02.044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A new method with an efficient algorithm is developed for computing the Lyapunov constants of planar switching systems, and then applied to study bifurcation of limit cycles in a switching Bautin system. A complete classification on the conditions of a singular point being a center in this Bautin system is obtained. Further, an example of switching systems is constructed to show the existence of 10 small-amplitude limit cycles bifurcating from a center. This is a new lower bound of the maximal number of small-amplitude limit cycles obtained in quadratic switching systems near a singular point. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：1203 / 1226

页数：24

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