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The effect of dispersal on permanence in a predator-prey population growth model. (English) Zbl 1032.92032
Summary: We consider a periodic predator-prey system where the prey can disperse between one patch with a low level of food and without predation and one patch with a higher level of food but with predation. We assume Volterra within-patch dynamics. Under the assumption that the average of the dispersal rate from Patch 1 to Patch 2 is less than that of the intrinsic growth rate of prey in Patch 1, we provide a sufficient and necessary condition to guarantee the prey and predator species to be permanent by using the main techniques of Z. Teng, Appl. Anal. 72, 339-352 (1999; Zbl 1031.34045).
34C60Qualitative investigation and simulation of models (ODE)
34C25Periodic solutions of ODE
34D05Asymptotic stability of ODE
37N25Dynamical systems in biology