Pattern formation in a predator-mediated coexistence model with prey-taxis. (English) Zbl 1509.35035
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.
MSC:
| 35B36 | Pattern formations in context of PDEs |
| 35B32 | Bifurcations in context of PDEs |
| 35K59 | Quasilinear parabolic equations |
| 92D25 | Population dynamics (general) |
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