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2015•Journal of Natural Science of Heilongjiang UniversityRequires access

Hopf bifurcation of ratio-dependent predator-prey model

Li B

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Abstract

Hopf bifurcation of ratio-dependent predator-prey model with diffusion and homogeneous Neumann boundary condition is considered. By choosing an appropriate bifurcation parameter,the existence of Hopf bifurcations at the positive equilibrium is established. When the spatial domain is chosen to be the interval( 0,π),conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution is derived by using the normal form theory and the center manifold theorem.

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What this paper is about

Hopf bifurcation of ratio-dependent predator-prey model with diffusion and homogeneous Neumann boundary condition is considered. By choosing an appropriate bifurcation parameter,the existence of Hopf bifurcations at the positive equilibrium is established. When the spatial domain is chosen to be the interval( 0,π),conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution is derived by using the normal form theory and the center manifold theorem.

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Available abstract

Hopf bifurcation of ratio-dependent predator-prey model with diffusion and homogeneous Neumann boundary condition is considered. By choosing an appropriate bifurcation parameter,the existence of Hopf bifurcations at the positive equilibrium is established. When the spatial domain is chosen to be the interval( 0,π),conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution is derived by using the normal form theory and the center manifold theorem.

Key concepts: Mathematics, Hopf bifurcation, Center manifold, Saddle-node bifurcation, Neumann boundary condition, Pitchfork bifurcation, Mathematical analysis, Transcritical bifurcation

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