Delay differential systems with time-varying delay: new directions for stability theory
Delay differential systems with time-varying delay: new directions for stability theory
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时变时滞的时滞微分系统：稳定性理论的新方向
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
J. Louisell
中科院分区：
文献类型：
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作者：
J. Louisell
本文给出了具有时变时滞的常系数时滞微分方程的Markus-Yamabe不稳定性的一个例子。对于时滞函数值域的所有值，关联自治时滞方程的特征函数都是指数稳定的。然而，时变系统的基本解是无界的。我们还给出了一个具有绝对连续时滞函数的修正实例，可以很容易地计算出时滞函数的平均变分，然后将这个平均变分与作者先前关于具有时变时滞的时滞微分方程稳定性指数保持的工作联系起来。通过这种方式，我们提出了一种关于马库斯-山部不稳定性条件的可能观点。最后，我们给出了一个非常简单的不稳定性猝灭的例子。为了提出对淬火现象条件的看法，我们将其与Cooke早期关于具有时变延迟的延迟系统中谱动力学保持的工作联系起来。
In this paper we give an example of Markus–Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example having absolutely continuous delay function, easily calculating the average variation of the delay function, and then relating this average to earlier work of the author on preservation of the stability exponent in delay differential equations with time-varying delay. In this way we suggest one possible viewpoint on the conditions for Markus–Yamabe instability. Finally, we give a very brief sketch of an example of quenching of instability. To suggest a view on conditions for quenching phenomena, we relate this to earlier work of Cooke on preservation of spectral dynamics in delay systems having time-varying delay.