关键词: Hopf bifurcation, stability, time delay, predator-prey system, periodic solution

Abstract: In this paper, a predator-prey model of three species is investigated, the necessary and sufficient of the stable equilibrium point for this model is studied. Further, by introducing a delay as a bifurcation parameter, it is found that Hopf bifurcation occurs when τ cross some critical values. And, the stability and direction of hopf bifurcation are determined by applying the normal form theory and center manifold theory. numerical simulation results are given to support the theoretical predictions. At last, the periodic solution of this system is computed.

Key words: Hopf bifurcation, stability, time delay, predator-prey system, periodic solution