View in EDS

Center Manifolds and Normal Forms for Nonlinearly Periodically Forced DDEs.

Saved in:
Bibliographic Details
Title: Center Manifolds and Normal Forms for Nonlinearly Periodically Forced DDEs.
Authors: Lentjes, Bram1 (AUTHOR) bram.lentjes@uhasselt.be, Daniëls, Seppe2 (AUTHOR) seppe.daniels@student.kuleuven.be, Follon, Meinder3 (AUTHOR) m.follon@student.tudelft.nl, Kuznetsov, Yuri A.4,5 (AUTHOR) i.a.kouznetsov@uu.nl
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Aug2026, Vol. 36 Issue 10, p1-31. 31p.
Subjects: Center manifolds (Mathematics), Normal forms (Mathematics), Hopf bifurcations, Delay differential equations, Bifurcation theory, Functional analysis
Abstract: The aim of this paper is to provide an effective framework for analyzing bifurcations of equilibria in nonlinearly periodically forced delay differential equations. First, we establish the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic equilibrium using the rigorous functional analytic framework of dual semi-groups (sun-star calculus). Second, we construct a center manifold parametrization that allows us to describe the local dynamics on the center manifold near the equilibrium in terms of periodically forced normal forms. Third, we present a normalization method to derive explicit computational formulas for the critical normal form coefficients at a bifurcation of interest. In particular, we obtain such formulas for the periodically forced fold and nonresonant Hopf bifurcation. Several examples and indications from the literature confirm the validity and effectiveness of our approach. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 193982400
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Center Manifolds and Normal Forms for Nonlinearly Periodically Forced DDEs.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Lentjes%2C+Bram%22">Lentjes, Bram</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> bram.lentjes@uhasselt.be</i><br /><searchLink fieldCode="AR" term="%22Daniëls%2C+Seppe%22">Daniëls, Seppe</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> seppe.daniels@student.kuleuven.be</i><br /><searchLink fieldCode="AR" term="%22Follon%2C+Meinder%22">Follon, Meinder</searchLink><relatesTo>3</relatesTo> (AUTHOR)<i> m.follon@student.tudelft.nl</i><br /><searchLink fieldCode="AR" term="%22Kuznetsov%2C+Yuri+A%2E%22">Kuznetsov, Yuri A.</searchLink><relatesTo>4,5</relatesTo> (AUTHOR)<i> i.a.kouznetsov@uu.nl</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Bifurcation+%26+Chaos+in+Applied+Sciences+%26+Engineering%22">International Journal of Bifurcation & Chaos in Applied Sciences & Engineering</searchLink>. Aug2026, Vol. 36 Issue 10, p1-31. 31p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Center+manifolds+%28Mathematics%29%22">Center manifolds (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Normal+forms+%28Mathematics%29%22">Normal forms (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink><br /><searchLink fieldCode="DE" term="%22Delay+differential+equations%22">Delay differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Functional+analysis%22">Functional analysis</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The aim of this paper is to provide an effective framework for analyzing bifurcations of equilibria in nonlinearly periodically forced delay differential equations. First, we establish the existence of a periodic smooth finite-dimensional center manifold near a nonhyperbolic equilibrium using the rigorous functional analytic framework of dual semi-groups (sun-star calculus). Second, we construct a center manifold parametrization that allows us to describe the local dynamics on the center manifold near the equilibrium in terms of periodically forced normal forms. Third, we present a normalization method to derive explicit computational formulas for the critical normal form coefficients at a bifurcation of interest. In particular, we obtain such formulas for the periodically forced fold and nonresonant Hopf bifurcation. Several examples and indications from the literature confirm the validity and effectiveness of our approach. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Bifurcation & Chaos in Applied Sciences & Engineering is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193982400
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/S0218127426501427
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 31
        StartPage: 1
    Subjects:
      – SubjectFull: Center manifolds (Mathematics)
        Type: general
      – SubjectFull: Normal forms (Mathematics)
        Type: general
      – SubjectFull: Hopf bifurcations
        Type: general
      – SubjectFull: Delay differential equations
        Type: general
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Functional analysis
        Type: general
    Titles:
      – TitleFull: Center Manifolds and Normal Forms for Nonlinearly Periodically Forced DDEs.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Lentjes, Bram
      – PersonEntity:
          Name:
            NameFull: Daniëls, Seppe
      – PersonEntity:
          Name:
            NameFull: Follon, Meinder
      – PersonEntity:
          Name:
            NameFull: Kuznetsov, Yuri A.
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 02181274
          Numbering:
            – Type: volume
              Value: 36
            – Type: issue
              Value: 10
          Titles:
            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
              Type: main
ResultId 1