Pattern formation in a predator-mediated coexistence model with prey-taxis

Abstract

Can foraging by predators or a repulsive prey defense mechanism upset predator-mediated coexistence? This paper investigates one scenario in- volving a prey-taxis by a prey species. We study a system of three populations involving two competing species with a common predator. All three popu- lations are mobile via random dispersal within a bounded spatial domain, but the predator's movement is inuenced by one prey's gradient representing a repulsive effect on the predator. We prove existence of positive solutions, and investigate pattern formation through bifurcation analysis and numerical simulation.