Analysis of a prey-predator system incorporating the additive Allee effect and intraspecific cooperation

Abstract

To understand the influence of the Allee effect and intraspecific cooperation on the dynamics of a predator-prey system, we constructed a model using ordinary differential equations. Our research shows that the system exhibits more complex dynamics, including possible bistability between alternative semi-trivial states and an Allee effect for prey. The Allee effect can destabilize the system. The equilibrium points of the system could change from stable to unstable. Otherwise, even if the system were stable, it would take much longer time to reach a stable state. We also find that the presence of the Allee effect of prey increases the positive equilibrium density of the predator but has no effect on the positive equilibrium density of the prey. It should be noted that the influence of nonlinear predator mortality also causes the system to take a longer time to reach a steady state.

Keywords

• prey-predator
• allee effect
• intraspecific cooperation
• stability
• bifurcation