Optimal harvesting for a stochastic competition system with stage structure and distributed delay

A stochastic competition system with harvesting and distributed delay is investigated, which is described by stochastic differential equations with distributed delay. The existence and uniqueness of a global positive solution are proved via Lyapunov functions, and an ergodic method is used to obtain that the system is asymptotically stable in distribution. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of the stochastic competition system are established. We thereby obtain the optimal harvest strategy and maximum net economic revenue by the optimal harvesting theory of differential equations.