Stationary distribution and periodic solution of a stochastic Nicholson's blowflies model with distributed delay

Due to the complex set of abiotic and biotic interaction variables in the ecosystems, the dynamics of animal populations are generally considered to be driven in astate-dependent manner. This paper presents an analysis of a stochastic Nicholson's blowflies model with distributed delay, which consists of the existence and uniqueness of globally positive solution, extinction, existence of positive T-periodic solution and positive recurrence. Our results suggest that a smaller white noise is necessary to cause the existence of positive T-periodic solution and positive recurrence of the stochastic model, while a larger white noise will accelerate the extinction of the population. In addition, numerical simulation is used to support our main results.