一类具有毒性作用与双成熟时滞的非自治阶段竞争系统全局稳定性分析

In this paper, a nonautonomous stage structured two-species competitive system with toxic effect and double time delays is investigated due to maturation for two species, where toxic effect of toxin liberating species on nontoxic species is considered and theinhibiting effect is zero in absence of either species. Positivity and boundedness of solutions are analytically studied. By utilizing some comparison arguments, an iterative technique is proposed to discuss permanence of the species within competitive system. Furthermore, existence of positive periodic solutions is investigated based on continuation theorem of coincidence degree theory. By constructing an appropriate Lyapunov functional, sufficient conditions for global stability of the unique positive periodic solution are analyzed. Numerical simulations are carried out to show consistency with theoretical analysis.