Dynamics in a slow-fast Leslie-Gower predator-prey model with Beddington-DeAngelis functional response

This paper deals with a class of slow-fast Leslie-Gower predator-prey model with Beddington-DeAngelis functional response function. When predator reproduces much slower than prey, the explicit conditions for the local stability of all possible equilibria are given and the permanence of the model for all parameter values is proved. Under the framework of geometric singular perturbation theory, we prove the existence of singular Hopf bifurcation, canard explosion and relaxation oscillation. By applying the method of variation of parameter and symbolic computations, and analyzing the sign of a very complicated binary function with radicals on an unbounded domain, we prove that the singular Hopf bifurcation is always supercritical. Furthermore, it is also proven that the cyclicity of canard cycle is 1 by using the modified slow divergence integrals. It is the first time to give the explicit expressions of the low order terms of singular Hopf bifurcation curve and maximum canard curve in slow-fast predator-prey systems. Numerical simulations are also carried out to support and illustrate our analytical results. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data