Hopy Bifurcation and Stability Analysis in a Predator-Prey Model with Distributed Delays

Hong Bing Chen

doi:10.4028/www.scientific.net/AMR.1049-1050.1400

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Hopy Bifurcation and Stability Analysis in a Predator-Prey Model with Distributed Delays

Abstract:

In this paper, A mathematical model of two species with stage structure and distributed delays is investigated, the necessary and sufficient of the stable equilibrium point are studied. Further, by analyze the associated characteristic equation, it is founded that Hopf bifurcation occurs when τ crosses some critical value. The direction of Hopf bifurcation as well as stability of periodic solution are studied. Using the normal form theory and center manifold method.