Perturbations and Hopf bifurcation of the planar discontinuous dynamical system

Akhmet M.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.60, no.1, pp.163-178, 2005 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 60 Issue: 1
  • Publication Date: 2005
  • Doi Number: 10.1016/j.na.2004.08.029
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.163-178
  • Keywords: planar dynamical systems, discontinuous systems, focus, centre, stability, Hopf bifurcation, STABILITY
  • Middle East Technical University Affiliated: Yes

Abstract

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.