In this paper, a three-species Lotka-Volterra food-chain model with spatial diffusion and time delays is investigated. We first analyze the local stability of the steady states and the existence of Hopf bifurcation to this system under homogeneous Neumann boundary conditions. We consider the effects of impulses on the dynamics of the above food-chain model without spatial diffusion. Numerical simulations show that the system with constant periodic impulsive perturbations admits rich complex dynamics.

Key words: Hopf bifurcation, food chain, reaction diffusion, delay, stability, chaos.