Dynamical Analysis of a Delayed Diffusive Predator–Prey Model with Additional Food Provided and Anti-Predator Behavior

Abstract

We studied a delayed predator–prey model with diffusion and anti-predator behavior. Assume that additional food is provided for predator population. Then the stability of the positive equilibrium is considered. The existence of Hopf bifurcation is also discussed based on the Hopf bifurcation theory. The property of Hopf bifurcation is derived through the theory of center manifold and normal form method. Finally, we analyze the effect of time delay on the model through numerical simulations.

Keywords

• delay
• diffusion
• predator–prey
• Hopf bifurcation