Dynamical behavior of a ratio dependent predator-prey system with distributed delay

Celik C.

Discrete and Continuous Dynamical Systems - Series B, vol.16, no.3, pp.719-738, 2011 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.3934/dcdsb.2011.16.719
  • Journal Name: Discrete and Continuous Dynamical Systems - Series B
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.719-738


In this paper, we consider a predator-prey system with distributed time delay where the predator dynamics is logistic with the carrying capacity proportional to prey population. In [1] and [2], we studied the impact of the discrete time delay on the stability of the model, however in this paper, we investigate the effect of the distributed delay for the same model. By choosing the delay time tau as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay time tau passes some critical values. Using normal form theory and central manifold argument, we establish the direction and the stability of Hopf bifurcation. Some numerical simulations for justifying the theoretical analysis are also presented.