The Applications of Algebraic Methods on Stable Analysis for General Differential Dynamical Systems with Multidelays

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 imagi...

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Bibliographic Details
Main Authors: Jian Ma, Baodong Zheng
Format: Article
Language:English
Published: Wiley 2015-01-01
Series:Discrete Dynamics in Nature and Society
Online Access:http://dx.doi.org/10.1155/2015/984323
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Summary: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.
ISSN:1026-0226
1607-887X