On stability and bifurcation of periodic solutions of delay differential equations

The purpose of this paper is to study a class of delay differential equations with two delays. first, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the correlocal sta...

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Bibliographic Details
Published inJournal of applied mathematics & computing Vol. 19; no. 1-2; pp. 281 - 295
Main Authors El-Sheikh, M. M. A., El-Mahrouf, S. A. A.
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Nature B.V 01.03.2005
Subjects
Applied mathematics
Bifurcations
Computation
Delay
Differential equations
Eigenvalues
Eigenvectors
Mathematical analysis
Mathematical models
Response time
Stability
Stability analysis
Studies
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Summary:The purpose of this paper is to study a class of delay differential equations with two delays. first, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the correlocal stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:1598-5865
1865-2085
DOI:10.1007/BF02935805