Dynamics and pattern formation in homogeneous diffusive predator-prey systems with predator interference or foraging facilitation

We study a general diffusive predator-prey system under Neumann boundary conditions. First, we examine the global attractor and persistence of the system, which characterize the long-time behavior of the time-dependent solution, and the stability of all nonnegative equilibria of the system. Then, by analyzing the associated characteristic equation, we derive explicit conditions for the existence of Hopf bifurcation and Turing instability. Furthermore, the existence and nonexistence of nonconstant positive steady states of this model are studied by considering the effect of large diffusivity. Finally, to verify our theoretical results, the selected numerical simulations are included. The results show that under the effect of diffusion, the system shows different spatial patterns that can be stationary, periodic and chaotic. (C) 2019 Elsevier Ltd. All rights reserved.