ON THE BIFURCATION BEHAVIOR OF A THREE-SPECIES LOTKA-VOLTERRA FOOD CHAIN MODEL WITH TWO DISCRETE DELAYS

In this paper, a three-species Lotka-Volterra food chain model with two discrete delays is investigated, where the time delays are regarded as parameters. Its dynamics are studied in terms of local analysis and Hopf bifurcation analysis. By analyzing the associated characteristic transcendental equation, it is found that Hopf bifurcation occurs when these delays pass through a sequence of critical value. Sonic explicit formulae for determining the stability and the direction of the Hopf bifurcation periodic solutions are derived by using the normal form theory and center manifold theory. Finally, numerical simulations supporting the theoretical analysis are carried out.