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Zbl 1061.92058
Chen, Fengde
On a nonlinear nonautonomous predator--prey model with diffusion and distributed delay. (English)
[J] J. Comput. Appl. Math. 180, No. 1, 33-49 (2005). ISSN 0377-0427

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.

MSC 2000:: *92D40 Ecology
34D23 Global stability
34C27 Almost periodic solutions of ODE
34D05 Asymptotic stability of ODE

Keywords: Nonautonomous; Predator-prey; Continuous distributed delay; Almost periodic solution; Diffusion; Global asymptotic stability

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Zentralblatt MATH Berlin [Germany]