论文标题
多延迟微分方程：泰勒扩展方法
Multi-Delay Differential Equations: A Taylor Expansion Approach
论文作者
论文摘要
已经很充分理解的是，只有单个恒定延迟的许多延迟微分方程根据与临界延迟值相关的延迟值表现出稳定性的变化。为关键延迟找到一个公式对于理解延迟系统的动态非常重要，并且在系统仅具有单个恒定延迟时通常很容易获得。但是，如果我们考虑一个具有多个恒定延迟的系统，则没有已知的方法来获得这样的公式，该公式确定延迟的延迟值发生的变化会发生什么。在本文中，我们向通过Taylor扩展获得的多延迟系统以及其关键延迟的公式提供了一些单延迟近似值，该系统用于近似于多层系统中稳定性发生变化的位置。我们确定我们的近似值何时表现良好，并对两层和三层设置给予额外的分析和数值关注。
It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the critical delay is important to understanding the dynamics of delayed systems and is often simple to obtain when the system only has a single constant delay. However, if we consider a system with multiple constant delays, there is no known way to obtain such a formula that determines for what values of the delays a change in stability occurs. In this paper, we present some single-delay approximations to a multi-delay system obtained via a Taylor expansion as well as formulas for their critical delays which are used to approximate where the change in stability occurs in the multi-delay system. We determine when our approximations perform well and we give extra analytical and numerical attention to the two-delay and three-delay settings.
