Hopf bifurcation for a 3D filippov system


AKHMET M., Aruǧaslan D., Turan M.

Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis, vol.16, no.6, pp.759-775, 2009 (Peer-Reviewed Journal) identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 6
  • Publication Date: 2009
  • Journal Name: Dynamics of Continuous, Discrete and Impulsive Systems Series A: Mathematical Analysis
  • Journal Indexes: Scopus
  • Page Numbers: pp.759-775
  • Keywords: Center manifold, Filippov systems, Hopf bifurcation, Impulsive differential equations

Abstract

We study the behaviour of solutions for a 3-dimensional system of differential equations with discontinuous right hand side in the neighbourhood of the origin. Using B- equivalence of that system to an impulsive differential equation [3, 4], existence of a center manifold is proved, and then a Hopf bifurcation theorem is provided for such equations in the critical case. The results are apparently obtained for the systems with dimensions greater than two for the first time. Finally, an appropriate example is given to illustrate our results. Copyright © 2009 Watam Press.