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).


92D40 Ecology
34C60 Qualitative investigation and simulation of ordinary differential equation models
34C25 Periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
37N25 Dynamical systems in biology
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