Study of periodic diffusion and time delay induced spatiotemporal patterns in a predator-prey system

Abstract

In this paper, we establish a diffusion-reaction predator-prey model with Allee effect and time delay. For this model, we mainly study the effects of time delay and periodic diffusion on the stability of the equilibrium point and the formation of Turing pattern. First, we theoretically analyze the conditions of Turing instability caused by the time delay and periodic diffusion. At the same time, through a large number of numerical simulations, we verify the existence of spatiotemporal patterns and obtain that the pattern in the formation process not only appears the spots, strips, but also exists the coexistence of spots and strips. In addition, it also appears the labyrinth pattern under some suitable parameters. The final comparisons show that periodic diffusion, time delay and Allee effect all play an important role in the formation of Turing pattern.