Analysis of a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process

Abstract

In this paper, we propose and analyze a stochastic inshore–offshore hairtail fishery model with Ornstein–Uhlenbeck process, which is a stochastic non-autonomous system. Firstly, we show that there is a unique global solution to the stochastic system with any initial value. Then we study the pth moment boundedness and asymptotic pathwise estimation of the solutions of the stochastic system in turn. After that, we use a stochastic Lyapunov function method to obtain sufficient criteria for the existence of a stationary distribution of the stochastic model. Especially, under some appropriate conditions, it is noticed that we get the specific expression of the probability density of the linear system corresponding to the stochastic system. Finally, numerical simulations are presented to show the effectiveness of our conclusions.