Dynamics and pattern formations in diffusive predator-prey models with two prey-taxis

摘要

A reaction-diffusion two-predator-one-prey system with prey-taxis describes the spatial interaction and random movement of predator and prey species, as well as the spatial movement of predators pursuing preys. The global existence and boundedness of solutions of the system in bounded domains of arbitrary spatial dimension and any small prey-taxis sensitivity coefficient are investigated by the semigroup theory. The spatial pattern formation induced by the prey-taxis is characterized by the Turing type linear instability of homogeneous state; it is shown that prey-taxis can both compress and prompt the spatial patterns produced through diffusion-induced instability in two-predator-one-prey systems.