Article Contents

2011, Volume 16, Issue 3: 719-738. Doi: 10.3934/dcdsb.2011.16.719

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

Canan Çelik^1,

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

Received: April 2010

Revised: July 2010

Published: October 2011

Abstract / Introduction Related Papers Cited by

Abstract

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.

Keywords:

Mathematics Subject Classification: Primary: 34K18, 34K20, 37D25; Secondary: 92D25.

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