Abstract: The goal of this paper is to study systematically a food chain model consisting of one prey and two predator spacies. The authors show the interactions may lead to that two predators species are both extinct or one of them is extinct, or all three species may be coexistent in the form of positive steady state or oscillatory solutions. Using AMTLAB software, the authors present two examples to simulate these conclusions.

Key words: Global stability, Limit cycle, Persistence, Hopf bifurcations