Bifurcation of three-dimensional discontinuous cycles


AKHMET M., TURAN M.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.71, no.12, 2009 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 12
  • Publication Date: 2009
  • Doi Number: 10.1016/j.na.2009.03.071
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus

Abstract

We consider three-dimensional discontinuous dynamical systems with non-fixed moments of impacts. Existence of the center manifold is proved for the system. The result is applied for the extension of the planar Hopf bifurcation theorem [M.U. Akhmet, Perturbations and Hopf bifurcation of the planar discontinuous dynamical system, Nonlinear Analysis 60 (2005) 163-178]. Illustrative examples are constructed for the theory. (C) 2009 Elsevier Ltd. All rights reserved.