Stability and Hopf Bifurcation of a Diffusive Predator-Prey Model with Hyperbolic Mortality

The dynamics of a reaction-diffusion predator-prey model with hyperbolic mortality and Holling type II response effect is considered. The stability of the positive equilibrium and the existence of Hopf bifurcation are investigated by analyzing the distribution of eigenvalues without diffusion. We also study the spatially homogeneous and nonhomogeneous periodic solutions through all parameters of the system which are spatially homogeneous. To verify our theoretical results, some numerical simulations are also presented. (C) 2015 Wiley Periodicals, Inc.