Stability and Hopf Bifurcation in a Diffusive Predator-Prey System with Beddington-DeAngelis Functional Response and Time Delay

摘要

This paper is concerned with a diffusive predator-prey system with Beddington-DeAngelisfunctional response and delay effect. By analyzing the distribution of the eigenvalues, the stabilityof the positive equilibrium and the existence of spatially homogeneous and spatially inhomogeneousperiodic solutions are investigated. Also, it is shown that the small diffusion can affect the Hopfbifurcations. Finally, the direction and stability of Hopf bifurcations are determined by normal formtheory and center manifold reduction for partial functional differential equations.