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 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2009
  • Doi Number: 10.1016/j.chaos.2009.03.071
  • Title of Journal : CHAOS SOLITONS & FRACTALS
  • Page Numbers: pp.1474-1484


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.