Dynamical Analysis of a Stochastic Predator-Prey Model with an Allee Effect

Abstract

We present and analyze a modified Holling type-II predator-prey model that includes some important factors such as Allee effect, density-dependence, and environmental noise. By constructing suitable Lyapunov functions and applying Itô formula, some qualitative properties are given, such as the existence of global positive solutions, stochastic boundedness, and the global asymptotic stability. A series of numerical simulations to illustrate these mathematical findings are presented.