Abstract: A dynamics model of food chain for three species including prey, predator and toppredator is studied. The Monod-Haldance functional response is used in the food chain system. By applying qualitative analysis and Hopf bifurcation theory, criteria are derived for global stability of the boundary equilibria,
existence of periodic orbits and persistence of the system. To summarize and classify the global dynamics of the system, the parameters regions with different dynamics behavior are derived. According to the regions, the authors show that the system can lead to a very complicated dynamics behavior and present an example to illustrate the conclusions by using MATLAB software.

Key words: Food web, Global stability, Period orbit, Hopf bifurcation, Parameters regions