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Updated: Jan 19, 2026
Predator-Prey Interactions in the Ecosystem
A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing
Paulo Amorim1, Bruno Telch1, Luis M Villada2
1Instituto de Matemática, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C, Cidade Universitária - Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ - Brasil.
Abstract:
In this paper, we propose and analyze a reaction-diffusion model for predator-prey interaction, featuring both prey and predator taxis mediated by nonlocal sensing. Both predator and prey densities are governed by parabolic equations. The prey and predator detect each other indirectly by means of odor or visibility fields, modeled by elliptic equations. We provide uniform estimates in Lebesgue spaces which lead to boundedness and the global well-posedness for the system. Numerical experiments are presented and discussed, allowing us to showcase the dynamical properties of the solutions.
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