Dynamic analysis of a fast slow modified Leslie–Gower predator–prey model with constant harvest and stochastic factor

Abstract

In this paper, the dynamic properties of a fast slow modified Leslie–Gower predator–prey model with constant harvest are discussed. The results show that the system appears different Hopf bifurcations and limit cycles as parameters change, and the stability of the internal equilibriums changes accordingly. The system also appears Bogdanov–Takens bifurcation phenomenon. For the fast–slow system of this model, the second order approximate perturbation manifolds, and an approximate manifold passing the fold point are constructed. Then using the criterion of inflection point curve and blow-up method, the existence of canard cycles is analyzed. By comparing with the model with nonlinear harvest, the different effects of constant harvest on the model are highlighted. In addition, the effect of stochastic factors on the fast–slow system is considered.