LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

被引：3

作者：

Cardin, Pedro Toniol ^{[1
]}

De Carvalho, Tiago ^{[1
]}

Llibre, Jaume ^{[2
]}

机构：

[1] IBILCE UNESP, Dept Matemat, BR-15054000 Sao Paulo, Brazil

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

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2011年 / 21卷 / 11期

基金：

巴西圣保罗研究基金会;

关键词：

Discontinuous piecewise linear differential systems; limit cycles; averaging theory; BIFURCATION;

D O I：

10.1142/S0218127411030441

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the bifurcation of limit cycles from the periodic orbits of a two-dimensional (resp. four-dimensional) linear center in R-n perturbed inside a class of discontinuous piecewise linear differential systems. Our main result shows that at most 1 (resp. 3) limit cycle can bifurcate up to first-order expansion of the displacement function with respect to the small parameter. This upper bound is reached. For proving these results, we use the averaging theory in a form where the differentiability of the system is not needed.

引用

页码：3181 / 3194

页数：14

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