Global structure of a kind of predator-prey system

In this paper we prove a theorem, theorem 2, on nonexistence of closed trajectory for a general predator-prey system.Then, using this theorem and another theorem on existence and uniqueness of limit cycle for predator-prey system^1], we complete the investigation of a concrete model of predator-prey system^2] x=γx(1-x/K)-yxⁿ/(a+xⁿ) y=y(μxⁿ/(a+xⁿ)-D) (n=1,2) under the conditions of all kinds of parameters.