Piecewise linear differential systems without equilibria produce limit cycles?

被引：32
作者：
Llibre, Jaume [1 ]
Teixeira, Marco Antonio [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain
[2] Univ Estadual Campinas, Dept Matemat, Caixa Postal 6065, BR-13083970 Campinas, SP, Brazil
来源：
NONLINEAR DYNAMICS | 2017年 / 88卷 / 01期
基金：
巴西圣保罗研究基金会;
关键词：
Limit cycles; Continuous piecewise linear differential systems; Discontinuous piecewise differential systems; BIFURCATIONS;
D O I：
10.1007/s11071-016-3236-9
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
In this article, we study the planar piecewise differential systems formed by two linear differential systems separated by a straight line, such that both linear differential have no equilibria, neither real nor virtual. When the piecewise differential system is continuous, we show that the system has no limit cycles. But when the piecewise differential system is discontinuous, we show that it can have at most one limit cycle.
引用
收藏
页码：157 / 164
页数：8
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