Persistence of species in a predator-prey system with climate change and\n either nonlocal or local dispersal

Abstract

We are concerned with the persistence of both predator and prey in a\ndiffusive predator-prey system with a climate change effect, which is modeled\nby a spatial-temporal heterogeneity depending on a moving variable. Moreover,\nwe consider both the cases of nonlocal and local dispersal. In both these\nsituations, we first prove the existence of forced waves, which are positive\nstationary solutions in the moving frames of the climate change, of either\nfront or pulse type. Then we address the persistence or extinction of the prey\nand the predator separately in various moving frames, and achieve a complete\npicture in the local diffusion case. We show that the survival of the species\ndepends crucially on how the climate change speed compares with the minimal\nspeed of some pulse type forced waves.\n