标题： 一种通过等谱降维研究时变延迟微分方程稳定性的新方法 显示英文标题

标题： A New Approach to Stability of Delay Differential Equations with Time-Varying Delays via Isospectral Reduction

摘要： 理解时间延迟如何影响时滞微分方程的稳定性对于建模许多经历时间延迟的自然和技术系统非常重要。 在这里，我们引入了一种新的稳定性准则，称为内在稳定性，用于这些方程的时滞无关稳定性，表明了对于一大类非自治非线性系统具有全局指数稳定性。 我们的方法能够包含有界时变延迟，包括某些类型的不连续性。 我们采用的方法是新颖的，将时滞微分方程与一系列大小不断增加的有限维矩阵序列相关联，并使用同谱约简的图论技术来分析这个序列。 我们给出了这些结果在确定时滞储备计算机一致性问题中的应用。 显示英文摘要

摘要： Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for delay-independent stability of these equations, called intrinsic stability, showing global exponential stability for a large class of nonautonomous nonlinear systems. Our approach is able to incorporate bounded time-varying delays, including those with certain types of discontinuities. The approach we take to prove this result is novel, associating the delay differential equation with a sequence of finite-dimensional matrices of increasing size and using the graph-theoretic technique of isospectral reduction to analyze this sequence. We give an application of these results to the problem of determining consistency for delayed reservoir computers.