Stability and Hopf bifurcation in a diffusivepredator-prey system  incorporating a prey refuge

Xiaoyuan Chang; Junjie Wei

doi:10.3934/mbe.2013.10.979

Article Contents

2013, Volume 10, Issue 4: 979-996. Doi: 10.3934/mbe.2013.10.979

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Stability and Hopf bifurcation in a diffusive predator-prey system incorporating a prey refuge

Xiaoyuan Chang^1, and
Junjie Wei^1,

1.
Department of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001

Received: January 31, 2013

Revised: March 31, 2013

Published: May 2013

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Abstract

A diffusive predator-prey model with Holling type II functional response and the no-flux boundary condition incorporating a constant prey refuge is considered. Globally asymptotically stability of the positive equilibrium is obtained. Regarding the constant number of prey refuge $m$ as a bifurcation parameter, by analyzing the distribution of the eigenvalues, the existence of Hopf bifurcation is given. Employing the center manifold theory and normal form method, an algorithm for determining the properties of the Hopf bifurcation is derived. Some numerical simulations for illustrating the analysis results are carried out.

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Mathematics Subject Classification: Primary: 35Q92, 35B32; Secondary: 35B35.

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