文章基本信息

标题：The Applications of Algebraic Methods on Stable Analysis for General Differential Dynamical Systems with Multidelays
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作者：Jian Ma ; Baodong Zheng
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2015
卷号：2015
DOI：10.1155/2015/984323
出版社：Hindawi Publishing Corporation
摘要：The distribution of purely imaginary eigenvalues and stabilities of generally singular or neutral differential dynamical systems with multidelays are discussed. Choosing delays as parameters, firstly with commensurate case, we find new algebraic criteria to determine the distribution of purely imaginary eigenvalues by using matrix pencil, linear operator, matrix polynomial eigenvalues problem, and the Kronecker product. Additionally, we get practical checkable conditions to verdict the asymptotic stability and Hopf bifurcation of differential dynamical systems. At last, with more general case, the incommensurate, we mainly study critical delays when the system appears purely imaginary eigenvalue.