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

Paulo Amorim | Zendy; Bruno Telch | Zendy; Luis Miguel Villada | Zendy

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

Author(s) -

Paulo Amorim,

Bruno Telch,

Luis Miguel Villada

Publication year - 2019

Publication title -

mathematical biosciences and engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.451

H-Index - 45

eISSN - 1551-0018

pISSN - 1547-1063

DOI - 10.3934/mbe.2019257

Subject(s) - predator , predation , pursuit evasion , reaction–diffusion system , mathematics , diffusion , taxis , statistical physics , mathematical analysis , physics , mathematical optimization , ecology , biology , thermodynamics , botany

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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