Hopf Bifurcation Analysis of a Delayed Diffusive Predator-Prey Model with Predator Interference or Foraging Facilitation

Abstract

A delayed diffusive predator-prey model with predator interference or foraging facilitation is studied. We are interested in the existence of Turing instability, local stability, and Hopf bifurcation. We analyze the direction and stability of bifurcating periodic solutions by the normal form method. Our results suggest that diffusion can induce Turing instability and time delay can induce oscillation of prey and predator’s densities. In addition, the interference parameter λ0 has stabilizing and destabilizing effect on the positive equilibrium.