Relaxation oscillation and canard explosion in a slow–fast predator–prey model with Beddington–DeAngelis functional response

Abstract

In this paper, we consider a predator–prey model with Beddington–DeAngelis functional response. Considering the predator’s rate of growth and death is much lower than that of prey’s, the model becomes a slow–fast system that mathematically leads to a singular perturbation problem. Using geometric singular perturbation theory due to Fenichel and blow up technique, we have investigated the system and obtained very rich and complicated dynamical phenomena including the existence of relaxation oscillation, canard cycles near the Hopf bifurcation point and the interesting phenomenon of canard explosion.