Abstract In this paper we extend the classical “decomposing+embedding” method for systems of delay differential equations. Our extension has two advantages: (1) enhancing the range of applicability of the classical method and (2) providing delay dependent criteria of global attraction. The leading ideas are, on the one hand, the extension of the notion of dominance introduced first for difference equations and, on the other hand, the use of some monotone ideas developed by H.L. Smith and collaborators. We apply our results to some classical models of population dynamics, mainly models with patch structure.

中文翻译：

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具有混合单调性的延迟微分方程系统中的全局吸引力准则

摘要 在本文中，我们扩展了延迟微分方程组的经典“分解+嵌入”方法。我们的扩展有两个优点：（1）增强了经典方法的适用范围；（2）提供了全球吸引力的延迟相关标准。主要思想一方面是对差分方程首先引入的支配性概念的扩展，另一方面是使用由 HL Smith 及其合作者开发的一些单调思想。我们将我们的结果应用于一些经典的种群动态模型，主要是具有补丁结构的模型。