Abstract：Based on the ecosystem with functional response, a differential ecosystem with functional response is established with the application of mathematic ecology. The system is discussed by using differential equations qualities theory. The system＇s equilibrium points are studied. The degree and the stability of the center focus are analyzed. The existence zone of the system＇s limit cycle is given. By using Bendixson theorem and Zhang Zhi-fen theorem, the existence and uniqueness of the system＇s limit cycle are proved if the given parameters satisfy certain conditions. It shows that the densities of preys and predators are stable under some conditions.
2008, Vol. 29 
