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Persistence and global stability for nonautonomous predator-prey system with diffusion and time delay. (English) Zbl 0903.92029
Summary: A nonautonomous predator-prey model with diffusion and continuous time delay is studied, where all parameters are time-dependent. The system, which is composed of two Lotka-Volterra patches, has two species: one can diffuse between two patches, but the other is confined to one patch and cannot diffuse. It is proved that the system is uniformly persistent under appropriate conditions. Furthermore, sufficient conditions are established for global stability of the system.
MSC:
92D40Ecology
34K20Stability theory of functional-differential equations
34K25Asymptotic theory of functional-differential equations