The applications of algebraic methods on stable analysis for general differential dynamical systems with multidelays
type: Item
instance of: scholarly article
title: The applications of algebraic methods on stable analysis for general differential dynamical systems with multidelays
zbMATH Open document ID: 1418.34133
DOI: 10.1155/2015/984323
author: Jian Ma
author: Baodong Zheng
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K06
Mathematics Subject Classification ID: 34K18
zbMATH DE Number: 7025576
Wikidata QID: Q59105616
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/984323
OpenAlex ID: W1594184450
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description: scientific article; zbMATH DE number 7025576