The joint effects of diffusion and delay on the stability of a ratio-dependent predator-prey model

This paper is concerned with a diffusive and delayed predator-prey system with Leslie-Gower and ratio-dependent Holling type III schemes subject to homogeneous Neumann boundary conditions. Preliminary analyses on the well-posedness of solutions and the dissipativeness of the system are presented with assistance of inequality technique. Then the Hopf bifurcation induced by spatial diffusion and time delay is discussed, respectively. Moreover, the bifurcation properties are obtained by computing the norm forms on the center manifold. Finally, some numerical simulations and conclusions are given to verify and illustrate the theoretical results.