Deterministic and stochastic analysis of a modified Leslie–Gower predator–prey model with Holling‐type II functional response

Abstract

This paper aims to study the deterministic and stochastic features of a modified Leslie–Gower predator–prey model with Holling‐type II functional response. We first investigate the dynamical properties of the deterministic model, including existence and stability of the equilibrium, and different types of bifurcations. For the stochastic model, a phenomenon of noise‐induced state transition is found. By applying the stochastic sensitivity functions technique, we construct the confidence domain of stochastic attractor and then estimate the critical value of the intensity of noise generating this transition. Numerical simulations are performed to validate the analytical findings.