Complex dynamics and optimal harvesting for a stochastic food-web model with intraguild predation and time delays

This paper is concerned with a stochastic three species food-web model with intraguild predation and time delays. First, we show the existence of a unique global positive solution. Next, the sufficient conditions for extinction and persistence in mean of each population are established. Then, we show the model is stable in distribution. Next, sufficient criteria for the existence of optimal harvest are discussed. Moreover, optimal harvest effort and maximum harvest yield are obtained. In addition, we show the effects of stochastic perturbations and intraguild predation on the persistence and extinction of each population. In the case of coexistence of three species, we also show the effects of white noise of all trophic levels on the mean abundance and optimal harvest effort of each population. Finally, some numerical simulations are given.