Dynamical Property Analysis of a Delayed Diffusive Predator-Prey Model with Fear Effect

Abstract

In this paper, we study a delayed diffusive predator-prey model with fear effect and Holling II functional response. The stability of the positive equilibrium is investigated. We find that time delay can destabilize the stable equilibrium and induce Hopf bifurcation. Diffusion may lead to Turing instability and inhomogeneous periodic solutions. Through the theory of center manifold and normal form, some detailed formulas for determining the property of Hopf bifurcation are presented. Some numerical simulations are also provided.