On the existence and uniqueness of limit cycles in planar continuous piecewise linear systems without symmetry

被引：102

作者：

Llibre, Jaume ^{[1
]}

Ordonez, Manuel ^{[2
]}

Ponce, Enrique ^{[2
]}

机构：

[1] Univ Autonoma Barcelona, Fac Ciencies, Dept Matemat, E-08193 Barcelona, Spain

[2] Escuela Tecn Super Ingn, Dept Matemat Aplicada, Seville 41092, Spain

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2013年 / 14卷 / 05期

关键词：

Piecewise linear systems; Lienard equation; Limit cycles; BIFURCATION SETS; OSCILLATIONS; EQUATIONS;

D O I：

10.1016/j.nonrwa.2013.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Some techniques to show the existence and uniqueness of limit cycles, typically stated for smooth vector fields, are extended to continuous piecewise-linear differential systems. New results are obtained for systems with three linearity zones without symmetry and having one equilibrium point in the central region. We also revisit the case of systems with only two linear zones giving shorter proofs of known results. A relevant application to the McKean piecewise linear model of a single neuron activity is included. (C) 2013 Elsevier Ltd. All rights reserved.

引用

页码：2002 / 2012

页数：11

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