关键词: 多时滞, 扩散项, 持久生存, Lyapunov函数, 全局吸引性, 概周期解

Abstract: A delays non-autonomous predator-prey model with predator diffusion is studied. By using comparison theorem of the differential equation, it is proven that the system is permanent; furthermore, by constructing a suitable Lyapunov function, the sufficient conditions which guarantee the existence of a unique global attractive positive almost periodic solution of the system are obtained; the feasibility of theoretical analysis is verified by using software of matlab examples of numerical simulation.

Key words: delays, diffusion, permanence, Lyapunov function, global attractivity, almost periodic solution