Global existence of solutions and uniform persistence of a diffusive predator–prey model with prey-taxis

Abstract

This paper proves the global existence and boundedness of solutions to a general reaction–diffusion predator–prey system with prey-taxis defined on a smooth bounded domain with no-flux boundary condition. The result holds for domains in arbitrary spatial dimension and small prey-taxis sensitivity coefficient. This paper also proves the existence of a global attractor and the uniform persistence of the system under some additional conditions. Applications to models from ecology and chemotaxis are discussed.