Hopf Bifurcation Analysis in a Diffusive Food-Chain Model with Two Time Delays.

In this paper, a food chain model with two time delays and diffusion is investigated. The local stability of the positive equilibrium is analyzed. By choosing the two time delays as the bifurcation parameter, the existence of Hopf bifurcation is studied. Using the normal form method and center manifold theorem, we can derive explicit formulas to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solution. Numerical simulations are carried out to illustrate our theoretical results.