Analysis of a stochastic Leslie-Gower three-species food chain system with Holling-II functional response and Ornstein-Uhlenbeck process

Abstract

This paper studies a stochastic Leslie-Gower model with a Holling-II functional response that is driven by the Ornstein-Uhlenbeck process. Some asymptotic properties of the solution of the stochastic Leslie-Gower model are introduced: The existence and uniqueness of the global solution of the model are given; the ultimate boundedness of the model is proven; by constructing the Lyapunov function and applying Ito's formula, the existence of the stationary distribution of the model is demonstrated; and the conditions for system extinction are discussed. Finally, numerical simulations are used to validate our conclusion.

Keywords

• leslie-gower model
• holling-ii functional response
• ornstein-uhlenbeck process
• stationary distribution
• extinction