Dynamics of a Leslie–Gower predator–prey model with additive Allee effect

Abstract

In this paper, we investigate the complex dynamics of a Leslie–Gower predation model with additive Allee effect on prey. Without Allee effect, the model has a unique globally asymptotically stable equilibrium point under some conditions. With Allee effect on prey, the model has none, one or two positive equilibria. Moreover, we prove the existence of parameter subsets for which the model can have Hopf bifurcation. And we find that when the model exhibits two positive equilibria there is a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. One of the most interesting findings is that Allee effect can increase the risk of ecological extinction.