PATTERN DYNAMICS OF A PREDATOR-PREY SYSTEM WITH IVLEV-TYPE FUNCTIONAL RESPONSE

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 respectively. Finally, we show some interesting spatiotemporal dynamical behaviors in numerical simulations. Our result is consistent with the “activation-inhibition” mechanism, where the prey is treated as an activator and the predator is treated as an inhibitor. When the diffusion rate of the prey is much lower than that of the predator, patterns may be generated.