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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.

35K59 Quasilinear parabolic equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
FEniCS; SyFi
Full Text: DOI
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