2012•Shuxue de shijian yu renshiRequires access

Stability and Hopf Bifurcation of a Predator-Prey Model

Feng Guanghui

Abstract

The stability and Hopf bifurcations of a predator-prey model with time delay and stage structure is investigated.By choosing time delay as the parameter,the stability of a positive equilibrium and the existence of Hopf bifurcations are established.Formulae determining the direction of bifurcations and the stability of bifurcating periodic solutions are given by using the normal form theory and center manifold theorem.

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Key concepts: Center manifold, Hopf bifurcation, Mathematics, Stability (learning theory), Pitchfork bifurcation, Biological applications of bifurcation theory, Manifold (fluid mechanics), Functional response