Turing patterns in a predator–prey model with double Allee effect

Abstract

In this paper, a predator–prey model with double Allee effect and self-diffusion terms is considered. The stability of the coexisting equilibrium is studied by analyzing the eigenvalue spectrum, and the spatial Turing patterns are investigated by using the method of multiple scale analysis. The amplitude equation is obtained, which shows that the system supports patterns like spots, stripes, hexagonal patterns and mixed-mode patterns. The influence of double Allee effect in system is discussed by the comparison of bifurcation diagrams. Finally, the numerical simulations have verified the correctness of above theoretical analysis and tell how the double Allee effect plays an important role in biological universe.