Analysis of a stochastic two-species Schoener's competitive model with Lévy jumps and Ornstein–Uhlenbeck process

Abstract

This paper studies a stochastic two-species Schoener's competitive model with Lévy jumps by the mean-reverting Ornstein–Uhlenbeck process. First, the biological implication of introducing the Ornstein–Uhlenbeck process is illustrated. After that, we show the existence and uniqueness of the global solution. Moment estimates for the global solution of the stochastic model are then given. Moreover, by constructing the Lyapunov function and applying Itô's formula and Chebyshev's inequality, it is found that the model is stochastic and ultimately bounded. In addition, we give sufficient conditions for the extinction of species. Finally, numerical simulations are employed to demonstrate the analytical results.

Keywords

• schoener's competitive model
• ornstein–uhlenbeck process
• extinction