Bifurcation Analysis for a Predator-Prey System with Prey Refuge and Diffusion

In this paper, a delayed predator-prey model incorporating a constant prey refuge and diffusion is studied. By analyzing the characteristic equation of linearized system corresponding to the model, we study the local asymptotic stability of the positive equilibrium of the system. Hopf bifurcation is occurred. By using the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, numerical simulations are performed to support the analytical results. With delay increasing, chaotic behaviors are observed.