Counting Roots of the Characteristic Equation for Linear Delay-Differential Systems
Counting Roots of the Characteristic Equation for Linear Delay-Differential Systems
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DOI：
10.1006/jdeq.1996.3127
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发表时间：
1997-05
影响因子：
2.4
通讯作者：
B.D Hassard
中科院分区：
文献类型：
--
作者：
B.D Hassard
摘要给出了一般实常系数线性时滞-微分系统特征方程正半平面上根数的计算公式。利用该公式建立了线性时滞微分系统零解渐近稳定的充分必要条件。该公式可用于验证自主时滞微分系统分岔分析中出现的稳定性假设。讨论了该公式在时滞-微分系统Hopf分岔理论中的应用，并给出了一个应用于双时滞方程的实例。
Abstract A formula is given that counts the number of roots in the positive half plane of the characteristic equation for general real, constant coefficient, linear delay-differential systems. The formula is used to establish necessary and sufficient conditions for asymptotic stability of the zero solution of linear delay-differential systems. The formula is potentially useful in verifying stability hypotheses that arise in bifurcation analysis of autonomous delay-differential systems. Application of the formula to Hopf bifurcation theory for delay-differential systems is discussed, and an example application to an equation with two delays is given.