Study on asymptotic behavior of stochastic Lotka–Volterra system in a polluted environment

Abstract

Abstract A three-species non-autonomous stochastic Lotka–Volterra food web system in a polluted environment is proposed, and the existence of positive periodic solutions of this system is established by constructing a proper Lyapunov function. Then the extinction property and its threshold between persistence and extinction are discussed by using Itô’s formula and the strong law of large numbers of martingale, and the sufficient condition of a.s. exponential stability of equilibrium point is obtained. Finally, the conclusions are tested by several numerical simulations.

Keywords

• Lotka–Volterra food web system
• Positive periodic solution
• Lyapunov function
• Exponential stability