A chemotaxis predator-prey model with indirect pursuit-evasion dynamics and parabolic signal

Abstract

We analyse a reaction-diffusion model for predator-prey interaction featuring both prey and predator taxis mediated by two signals. Both predator and prey densities are governed by parabolic equations, and the prey and predator detect each other indirectly by means of odor or visibility fields modelled by parabolic or elliptic equations – instead of only elliptic equations, as in earlier work. We prove the global well-posedness of the systems, as well as boundedness properties using the de Giorgi method and estimates in Lebesgue spaces. We also present some numerical simulations to illustrate the dynamical behaviour.