In this paper, a discrete ratio-dependent food-chain system with delay is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and the method of Lyapunov function, a set of sufficient conditions for the existence of positive periodic solutions and global asymptotic stability of the model are established.

中文翻译：

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具有比率的离散比例依赖链系统的周期特性和渐近行为

本文研究了具有时滞的离散比例依赖食物链系统。利用Gaines和Mawhin的重合度理论的连续定理和Lyapunov函数的方法，建立了存在正周期解和模型整体渐近稳定性的充分条件。