Hopf bifurcation of a ratio-dependent predator-prey system with time delay

Celik C.

CHAOS SOLITONS & FRACTALS, vol.42, no.3, pp.1474-1484, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2009
  • Doi Number: 10.1016/j.chaos.2009.03.071
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1474-1484
  • Yıldız Technical University Affiliated: No


In this paper, we consider a ratio dependent predator-prey system with time delay where the dynamics is logistic with the carrying capacity proportional to prey population. By considering the time delay as bifurcation parameter, we analyze the stability and the Hopf bifurcation of the system based on the normal form approach and the center manifold theory. Finally, we illustrate our theoretical results by numerical simulations. (C) 2009 Elsevier Ltd. All rights reserved.