Global stability analysis of a nonautonomous stage structured two prey-one predator system with interspecific competition and maturation delay

Abstract

In this paper, we investigate a nonautonomous two prey-one predator systems 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. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of solutions. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing some appropriate Lyapunov functionals, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.