Multidelay Differential Equations: A Taylor Expansion Approach
Multidelay Differential Equations: A Taylor Expansion Approach
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DOI：
10.1142/s0218127422500341
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发表时间：
2020-12
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影响因子：
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通讯作者：
Philip Doldo;Jamol Pender
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文献类型：
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作者：
Philip Doldo;Jamol Pender
众所周知，许多只有一个恒定时滞的时滞微分方程会根据相对于临界时滞值的延迟值而表现出稳定性的变化。求出临界时滞的公式对于理解时滞系统的动力学是很重要的，当系统只有一个恒定时滞时，这种公式往往很容易得到。然而，如果我们考虑一个具有多个恒定时滞的系统，没有已知的方法来获得这样的公式，该公式确定对于哪个时滞值发生稳定性变化。本文给出了通过泰勒展开得到的多时滞系统的一些单时滞近似，以及它们的临界时滞的公式，用来逼近多时滞系统中稳定性发生变化的位置。我们确定我们的近似何时执行得很好，并对两延迟和三延迟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 multidelay 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 multidelay system. We determine when our approximations perform well and we give extra analytical and numerical attention to the two-delay and three-delay settings.