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      Normal form of double-Hopf singularity with 1:1 resonance for delayed differential equations

      Author(s): 1 , 2
      Publication date (Electronic):
      Journal: Nonlinear Analysis: Modelling and Control
      Publisher: Vilnius University Press

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          Abstract

          In this manuscript, we provide a framework for the double-Hopf singularity with 1:1 resonance for general delayed differential equations (DDEs). The corresponding normal form up to the third-order terms is derived. As an application of our framework, a double-Hopf singularity with 1:1 resonance for a van der Pol oscillator with delayed feedback is investigated to illustrate the theoretical results.

          Most cited references20

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          A simple global characterization for normal forms of singular vector fields

          M.E. Brachet, P Coullet, G. Iooss … (1987)
          Article 0 comments Cited 43 times – based on 0 reviews     Review now
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            Normal Forms for Retarded Functional Differential Equations with Parameters and Applications to Hopf Bifurcation

            T. Faria, L.T. Magalhaes (1995)
            Article 0 comments Cited 33 times – based on 0 reviews     Review now
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              Normal Forms for Retarded Functional Differential Equations and Applications to Bogdanov-Takens Singularity

              L.T. Magalhaes, T. Faria (1995)
              Article 0 comments Cited 24 times – based on 0 reviews     Review now
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                Author and article information

                Journal
                Title: Nonlinear Analysis: Modelling and Control
                Publisher: Vilnius University Press
                ISSN (Electronic): 1392-5113
                Publication date Created: February 01 2019
                Publication date (Electronic): February 01 2019
                Volume: 24
                Issue: 2
                Pages: 241-260
                Affiliations
                [1 ]Department of Mathematics, Computer and Information Sciences, Mississippi Valley State University
                [2 ]Department of Mathematics, Kennesaw State University
                Article
                DOI: 10.15388/NA.2019.2.6
                SO-VID: 0e34d046-5623-4710-bd67-e10ad22eb6c1
                Copyright © © 2019
                License:

                All content is freely available without charge to users or their institutions. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission of the publisher or the author. Articles published in the journal are distributed under a http://creativecommons.org/licenses/by/4.0/.

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                ScienceOpen disciplines: Linguistics & Semiotics,Social & Behavioral Sciences,Law,Mathematics,History,Philosophy
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                ScienceOpen disciplines: Linguistics & Semiotics, Social & Behavioral Sciences, Law, Mathematics, History, Philosophy

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