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On a nonlinear nonautonomous predator–prey model with diffusion and distributed delay. (English) Zbl 1061.92058
Summary: A nonlinear nonautonomous predator-prey model with diffusion and continuous distributed delay is studied, where all the parameters are time-dependent. The system, which is composed of two patches, has two species: the prey can diffuse between the two patches, but the predator is confined to one patch. We first discuss the uniform persistence and global asymptotic stability of the model; after that, by constructing a suitable Lyapunov functional, some sufficient conditions for the existence of a unique almost periodic solution of the system are obtained. An example shows the feasibility of our main results.
34D23Global stability of ODE
34C27Almost and pseudo-almost periodic solutions of ODE
34D05Asymptotic stability of ODE