Relaxation Oscillations and Canard Explosion of a Leslie–Gower Predator–Prey System with Addictive Allee Effect

Abstract

In this paper, we consider the properties of a Leslie–Gower predator–prey system under two basic assumptions that the prey growth is affected by an addictive Allee effect, and the intrinsic growth rate of prey is much bigger than that of predator. Using the geometric singular perturbation theory and blow up technique, we show that this system can have rich dynamics, such as subcritical Hopf bifurcation, canard explosion and relaxation oscillations. Numerical simulations are also carried out to validate our analytical results.