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2013•Journal of Huaihai Institute of TechnologyRequires access

Stability and Hopf Bifurcation of a Predator-prey Model with Time Delay and Stage Structure

Lin Zhou

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Abstract

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

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What this paper is about

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

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Available abstract

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

Key concepts: Hopf bifurcation, Center manifold, Mathematics, Saddle-node bifurcation, Biological applications of bifurcation theory, Pitchfork bifurcation, Stability (learning theory), Period-doubling bifurcation

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