Dynamics of Leslie–Gower model with double Allee effect on prey and mutual interference among predators

Abstract

In this paper, a Leslie–Gower-type model is proposed to study a diffusive predator–prey system with multiple Allee effects acting on the growth rate of the prey population. Crowley–Martin-type functional response is considered to describe mutual interference among predators. Preliminary analysis includes uniqueness, dissipation and persistence property of the proposed model system. Detailed equilibrium analysis suggests that proposed system has rich dynamics in the sense that it can have four to eight equilibrium points. Multistability behavior is observed which is an interesting phenomenon. Parametric conditions are established for stability and Hopf bifurcation in both the local and diffusive systems. We investigate the emergence of complex patterns through Turing instability phenomenon of coupled reaction–diffusion system. A variety of patterns is obtained such as flower, square, circle and rhombus. Comparative analysis of patterns between weak and strong Allee effect is the novelty of this study. It is found that prey population uses its agility in aggregation. Bond between prey populations becomes stronger when the system experiences strong Allee effect which forces the predator population to remain united despite mutual interference. A highly significant result has been found that for slow prey population, predators decide the hunting strategy in a short time, while it takes more time for the predators to form a strategy to encircle the more dynamic prey.