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A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing

1 Instituto 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
2 GIMNAP-Departamento de Matemáticas, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile and CI2MA, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Special Issues: Mathematical Methods in the Biosciences

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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Keywords mathematical biology; predator-prey; mechanistic models; reaction-diffusion equations; numerical simulations; ecology; chemotaxis; animal movement

Citation: Paulo Amorim, Bruno Telch, Luis M. Villada. A reaction-diffusion predator-prey model with pursuit, evasion, and nonlocal sensing. Mathematical Biosciences and Engineering, 2019, 16(5): 5114-5145. doi: 10.3934/mbe.2019257


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