Permanence of a nonautonomous two prey-one predator system with stage structure and multiple time delays

In this paper, we investigate a nonautonomous two prey-one predator system with stage structure for each species. Interspecific competition between mature dominant prey and mature sub-dominant prey species are considered, and three discrete time delays are incorporated into the model due to maturation time for sub-dominant prey, dominant prey and predator species, respectively. By using differential system theory and comparison arguments, an iterative technique is proposed to discuss permanence of periodic solutions. Numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.