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

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.