View in EDS

Chaotic Dynamics of a Three-Dimensional Endomorphism in the Vicinity of the Arnold Tongue.

Saved in:
Bibliographic Details
Title: Chaotic Dynamics of a Three-Dimensional Endomorphism in the Vicinity of the Arnold Tongue.
Authors: Gharout, Hacene1 (AUTHOR) gharouthacene@gmail.com, Taha, Abdel-Kaddous2 (AUTHOR) taha@insa-toulouse.fr
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. May2026, Vol. 36 Issue 6, p1-33. 33p.
Subjects: Nonlinear dynamical systems, Endomorphisms, Chaos theory, Oscillations, Bifurcation theory, Hopf bifurcations
Abstract: The objective of this work is to investigate the transition between periodicity and chaos in the vicinity of Arnold tongues, within the framework of a three-dimensional, nonlinear, and noninvertible discrete dynamical system, which is a specific instance of an endomorphism. Arnold tongues, which represent families of resonance regions in the parameter space, are typically associated with the emergence of periodic orbits. As parameters vary and the system exits these regions, chaotic dynamics can emerge, notably through Neimark–Sacker bifurcations or period-doubling cascades. The analysis reveals alternating regimes of stability and chaos, highlighting how complex dynamics can arise at the boundaries of resonance zones in nonlinear systems. [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: 192586353
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Chaotic Dynamics of a Three-Dimensional Endomorphism in the Vicinity of the Arnold Tongue.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Gharout%2C+Hacene%22">Gharout, Hacene</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gharouthacene@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Taha%2C+Abdel-Kaddous%22">Taha, Abdel-Kaddous</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> taha@insa-toulouse.fr</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>. May2026, Vol. 36 Issue 6, p1-33. 33p.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Nonlinear+dynamical+systems%22">Nonlinear dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Endomorphisms%22">Endomorphisms</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The objective of this work is to investigate the transition between periodicity and chaos in the vicinity of Arnold tongues, within the framework of a three-dimensional, nonlinear, and noninvertible discrete dynamical system, which is a specific instance of an endomorphism. Arnold tongues, which represent families of resonance regions in the parameter space, are typically associated with the emergence of periodic orbits. As parameters vary and the system exits these regions, chaotic dynamics can emerge, notably through Neimark–Sacker bifurcations or period-doubling cascades. The analysis reveals alternating regimes of stability and chaos, highlighting how complex dynamics can arise at the boundaries of resonance zones in nonlinear systems. [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=192586353
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/S0218127426500665
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 33
        StartPage: 1
    Subjects:
      – SubjectFull: Nonlinear dynamical systems
        Type: general
      – SubjectFull: Endomorphisms
        Type: general
      – SubjectFull: Chaos theory
        Type: general
      – SubjectFull: Oscillations
        Type: general
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Hopf bifurcations
        Type: general
    Titles:
      – TitleFull: Chaotic Dynamics of a Three-Dimensional Endomorphism in the Vicinity of the Arnold Tongue.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Gharout, Hacene
      – PersonEntity:
          Name:
            NameFull: Taha, Abdel-Kaddous
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 02181274
          Numbering:
            – Type: volume
              Value: 36
            – Type: issue
              Value: 6
          Titles:
            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
              Type: main
ResultId 1