This paper deals with a class of Leslie-Gower predator-prey model with Beddington-DeAngelis functional response function. We assume that predator reproduce much slower than prey, which yield a slow-fast system. Using the normal form theory and geometric singular perturbation theory, we provide a detailed mathematical analysis for the existence of supercritical Hopf bifurcation, canard explosion and relaxation oscillation. Numerical simulations are also carried out to substantiate our analytical results.
2000 Mathematics Subject Classification: 34C37, 34C07, 37G15.