The stationary distribution and extinction of the n-dimensional stochastic Lotka-Volterra predator-prey system

In this paper, we discuss the existence of stationary distribution and extinction for n-dimensional stochastic Lotka-Volterra predator-prey system. By using Lyapunov methods and stochastic analysis techniques, sufficient criteria are obtained which ensure the existence of a stationary distribution for the stochastic predator-prey system. And sufficient conditions on the extinction are also established. Furthermore, the exponential extinction rate can be estimated precisely by the parameters of this system respectively. Finally, numerical experiments are conducted to validate the theoretical findings.