Predator invasion in predator-prey model with prey-taxis in spatially heterogeneous environment

We consider a predator-prey model with prey-taxis and Holling-type II functionalresponses in a spatially heterogeneous environment to analyze the effects of prey-taxis and the heterogeneity of an environment on predator invasion. To achieve ourgoal, we investigate the stability of semi-trivial solution in which the predator isabsent. It is known that both the predator diffusion and the death rate contributeto the predator invasion in a heterogeneous habitat when there is no prey-taxis.In this paper, we show that predator invasion is affected by the prey-taxis anddiffusions of the prey-taxis model for a certain range of predator death rates ina heterogeneous environment. Furthermore, in cases where predator invasion bypredator diffusion does not occur in a particular death rate range of the predator,predator invasion can occur by prey-taxis in a spatially heterogeneous habitat.In addition, we compare this phenomenon to the corresponding predator-preymodel with ratio-dependent functional responses. It is observed that none of thepredator's diffusion and prey-taxis affect the predator's invasion, and that onlythe predator's death rate contributes to predator invasion for the model withratio-dependent functional responses.(c) 2021 Elsevier Ltd. All rights reserved