Uniqueness of limit cycles for sewing planar piecewise linear systems

被引：51

作者：

Medrado, Joao C. ^{[1
]}

Torregrosa, Joan ^{[2
]}

机构：

[1] Univ Fed Goias, Inst Matemat & Estatist, BR-74001970 Goiania, Go, Brazil

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

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2015年 / 431卷 / 01期

关键词：

Non-smooth differential system; Uniqueness of limit cycle; Piecewise sewing planar linear differential system; BIFURCATION; EXISTENCE;

D O I：

10.1016/j.jmaa.2015.05.064

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper proves the uniqueness of limit cycles for sewing planar piece:wise linear systems with two zones separated by a straight line, Sigma, and only one Sigma-singularity of monodromic type. The proofs are based in an extension of Rolle's Theorem for dynamical systems on the plane. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：529 / 544

页数：16

共 22 条

[1]

Acary V., 2011, Lecture Notes in Electrical Engineering, V69

[2]

Andronov A. A., 1973, THEORY BIFURCATIONS

[3]

[Anonymous], 1988, MATH APPL SOVIET SER

[4] Piecewise linear differential systems with two real saddles [J].

Artes, Joan C. ;

Llibre, Jaume ;

Medrado, Joao C. ;

Teixeira, Marco A. .

MATHEMATICS AND COMPUTERS IN SIMULATION, 2014, 95 :13-22

[5] Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane [J].

Braga, Denis de Carvalho ;

Mello, Luis Fernando .

NONLINEAR DYNAMICS, 2013, 73 (03) :1283-1288

[6] PIECEWISE LINEAR PERTURBATIONS OF A LINEAR CENTER [J].

Buzzi, Claudio ;

Pessoa, Claudio ;

Torregrosa, Joan .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (09) :3915-3936

[7] Generic bifurcation of refracted systems [J].

Buzzi, Claudio A. ;

Medrado, Joao C. R. ;

Teixeira, Marco A. .

ADVANCES IN MATHEMATICS, 2013, 234 :653-666

[8] Degenerate Hopf bifurcations in discontinuous planar systems [J].

Coll, B ;

Gasull, A ;

Prohens, R .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 253 (02) :671-690

[9]

DiBernardo M, 2008, APPL MATH SCI, V163, P1, DOI 10.1007/978-1-84628-708-4

[10]

Dumortier F, 2006, UNIVERSITEXT, P1

← 1 2 3 →