Spatiotemporal Patterns and Bifurcation Analysis of a Diffusive Predator-prey Model with Prey Refuge

Abstract

In this paper, we examine a diffusive ratio dependent predator-prey model with prey refuge subject to Neumann boundary condition. We discuss the stability of the positive equilibrium and the existence of spatially homogeneous and inhomogeneous periodic solutions through distribution of the eigenvalues. The direction and stability of Hopf bifurcation are determined by the normal form theory and the center manifold theory. Finally numerical simulations are given to validate our analytical results.