Perturbations and Hopf bifurcation of the planar discontinuous dynamical system

被引：46

作者：

Akhmet, MU ^{[1
]}

机构：

[1] Middle E Tech Univ, Dept Math, TR-06531 Ankara, Turkey

[2] Middle E Tech Univ, Inst Appl Math, TR-06531 Ankara, Turkey

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2005年 / 60卷 / 01期

关键词：

planar dynamical systems; discontinuous systems; focus; centre; stability; Hopf bifurcation;

D O I：

10.1016/j.na.2004.08.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The objective of the paper is to obtain results on the behavior of a specific plane discontinuous dynamical system in the neighbourhood of the singular point. A new technique of investigation is presented. Conditions for existence of the foci and centres are proposed. The focus-centre problem and Hopf bifurcation are considered. Appropriate examples are given to ilustrate the bifurcation theorem. (C) 2004 Elsevier Ltd. All rights reserved.

引用

页码：163 / 178

页数：16

共 41 条

[1]

Akhmetov M. U., 1991, UKR MATH J, V43, P1209

[2]

AKHMETOV MU, 1992, DIFF EQUAT+, V28, P445

[3]

AKHMETOV MU, 1992, PMM-J APPL MATH MEC+, V56, P829

[4]

ANDRONOV VAA, 1966, THEORY OSCILLATIONS

[5]

[Anonymous], 1964, NONLINEAR DIFFERENTI

[6]

[Anonymous], PROBLEME GEN STABILI

[7]

[Anonymous], 1998, ARCH MATH BRNO

[8] Acceleration of one-dimensional mixing by discontinuous mappings [J].

Ashwin, P ;

Nicol, M ;

Kirkby, N .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2002, 310 (3-4) :347-363

[9]

BAUTIN NN, 1990, METHODS RULES QUALIT

[10]

Bohner M., 2001, Dynamic Equations on Time Scales: AnIntroduction With Applications, DOI DOI 10.1007/978-1-4612-0201-1

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