Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect

The Allee effect is widespread among endangered plants and animals in ecosystems, suggesting that a minimum population density or size necessary for survival. This paper investigates the stability pattern formation of predator–prey model with nonlinear reactive cross-diffusion under Neumann boundary conditions, which introduces effect. Firstly, ODE system asymptotically stable its positive equilibrium solution. In reaction self-diffusion, can destabilize system. Then, cross-diffusion, through linear analysis, coefficient used as bifurcation parameter, instability conditions driven by are obtained. Furthermore, we show (5) has at least one inhomogeneous stationary Finally, our theoretical results illustrated numerical simulations.