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Pattern formation in a predator-mediated coexistence model with prey-taxis. (English) Zbl 07208008
Summary: Can foraging by predators or a repulsive prey defense mechanism upset predator-mediated coexistence? This paper investigates one scenario involving a prey-taxis by a prey species. We study a system of three populations involving two competing species with a common predator. All three populations are mobile via random dispersal within a bounded spatial domain $$\Omega$$, but the predator’s movement is influenced 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.
Reviewer: Reviewer (Berlin)
##### MSC:
 35K59 Quasilinear parabolic equations 35Q92 PDEs in connection with biology, chemistry and other natural sciences 92D25 Population dynamics (general)
FEniCS; SyFi
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