# American Institute of Mathematical Sciences

October  2011, 16(3): 719-738. doi: 10.3934/dcdsb.2011.16.719

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

 1 Department of Mathematics and Computer Sciences, Bahçeşehir University, Istanbul, 34353, Turkey

Received  April 2010 Revised  July 2010 Published  June 2011

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.
Citation: Canan Çelik. Dynamical behavior of a ratio dependent predator-prey system with distributed delay. Discrete & Continuous Dynamical Systems - B, 2011, 16 (3) : 719-738. doi: 10.3934/dcdsb.2011.16.719
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##### References:
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