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Stabilizing effect of delay distribution for a class of second-order systems without instantaneous feedback

机译:一类无瞬时反馈的二阶系统时滞分布的稳定作用

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摘要

In many situations in physics, engineering and biology time delays arise naturally due to the time needed to transport information from one part of the system to another and/or to react to incoming information. When differential equations are used in the mathematical modelling, then incorporating time delays leads to a description by a delay differential equation. We consider here a class of second-order scalar delay equations without instantaneous feedback, where the delays enter according to a distribution function. This is a natural description whenever there is more than one delay. In this article we show that for this class of systems one can derive stability information about the distributed-delay system by considering the single-delay system where the delay is the mean delay of the distribution function. More specifically, we prove that the asymptotic stability of the zero solution of the second-order delay equation with symmetric delay distribution is implied by the stability of the associated mean-delay equation. Our proof is based on the comparison of stability charts of the two equations.
机译:在物理,工程和生物学的许多情况下,由于将信息从系统的一个部分传输到另一部分和/或对传入的信息做出反应需要时间,因此自然会产生时间延迟。当在数学建模中使用微分方程时,则合并时间延迟会导致使用延迟微分方程进行描述。我们在这里考虑一类没有瞬时反馈的二阶标量延迟方程,其中延迟根据分布函数输入。每当存在多个延迟时,这都是自然的描述。在本文中,我们表明对于此类系统,可以通过考虑时延为分布函数的平均时延的单时滞系统来导出有关时滞系统的稳定性信息。更具体地说,我们证明了相关的均值延迟方程的稳定性隐含具有对称延迟分布的二阶延迟方程零解的渐近稳定性。我们的证明是基于两个方程稳定性图表的比较。

著录项

  • 来源
    《Dynamical Systems》 |2011年第1期|p.85-101|共17页
  • 作者

    Gabor Kiss; Bernd Krauskopf;

  • 作者单位

    Department of Engineering Mathematics, University of Bristol, Bristol BS8 ITR, UK,Bolyai Institute, University of Szeged, Aradi vertanuk tere 1, H-6720 Szeged, Hungary;

    Bolyai Institute, University of Szeged, Aradi vertanuk tere 1, H-6720 Szeged, Hungary;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    delay differential equations; distributed delay; hybrid testing;

    机译:延迟微分方程;分布式延迟混合测试;
  • 入库时间 2022-08-17 13:08:36

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