The effect of dispersal on permanence in a predator-prey population growth model

In this paper, 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 a Volterra within-patch dynamic. Under the assumption that the average of 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 in [1].