Pattern dynamics of a predator-prey system with Ivlev-type functional response

Abstract In this paper, we study the dynamics and pattern formation of a reaction-diffusion system with Ivlev-type functional response and homogeneous Neumann boundary conditions. We first consider the global existence and boundedness of nonnegative solutions and then discuss the global stability of nonnegative steady states. By using the energy estimates and Leray-Schauder degree theory, we prove the nonexistence and existence of nonconstant positive steady states. We show some interesting spatiotemporal dynamical behaviors in numerical simulations. Our results suggest that the predator-prey system with Ivlev-type functional response enriches spatiotemporal dynamical behaviors.