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
收藏
页码：3181 / 3194
页数：14
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