Turing instability and pattern formation in a diffusive predator-prey system with opportunistic predators and weak Allee effect.

Abstract

In this paper, we investigate Turing instability in a diffusive predator-prey system with an opportunistic predator and a weak Allee effect in the prey population. We begin by applying the upper-lower solution method to establish the existence of positive solutions and to derive estimates for both the positive and steady-state solutions. We then show that diffusion can trigger Turing instability in the homogeneous steady states of the system. Numerical simulations are carried out to support the analytical results. In particular, we further examine a stochastic reaction-diffusion version of the model by introducing additive white noise. A comparison between the stochastic and deterministic cases reveals that white noise can enhance the stability of the system.