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Bifurcation and Chaos Analysis of Coupled Duffing Oscillators with Two-Periodic Excitations and Distributed Time Delays.

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Title: Bifurcation and Chaos Analysis of Coupled Duffing Oscillators with Two-Periodic Excitations and Distributed Time Delays.
Authors: Guo, Yu1 (AUTHOR) yuguodi5@163.com, Liu, Yicheng1 (AUTHOR) liuyc2001@hotmail.com
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. Mar2026, Vol. 36 Issue 3, p1-28. 28p.
Subjects: Bifurcation theory, Chaos theory, Duffing equations, Dynamical systems, Computer simulation, Stability theory
Abstract: This paper employs both analytical and numerical methods to investigate the dynamic characteristics of a coupled Duffing oscillators with two-periodic excitations and distributed time delays. First, the original system is transformed to an equivalent slow-coupled system using the fast–slow analysis method. The stability of equilibrium points and the pitchfork bifurcation phenomena resulting from changes in parameters are analyzed. Specifically, the relationship between the number of coupling layers and the stable equilibrium points is explored. Subsequently, the necessary conditions for the occurrence of chaos, such as homoclinic bifurcation leading to horseshoe chaos, are derived using the Melnikov method. By integrating phase diagrams with the largest Lyapunov exponent, we analyzed the influence of various parameters on chaotic trajectories. Additionally, the specific effects of system distribution delay intensity were further illustrated through numerical simulations. [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
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DbLabel: Engineering Source
An: 191297367
AccessLevel: 6
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PubTypeId: academicJournal
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  Label: Title
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  Data: Bifurcation and Chaos Analysis of Coupled Duffing Oscillators with Two-Periodic Excitations and Distributed Time Delays.
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  Data: <searchLink fieldCode="AR" term="%22Guo%2C+Yu%22">Guo, Yu</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yuguodi5@163.com</i><br /><searchLink fieldCode="AR" term="%22Liu%2C+Yicheng%22">Liu, Yicheng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> liuyc2001@hotmail.com</i>
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  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>. Mar2026, Vol. 36 Issue 3, p1-28. 28p.
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  Data: <searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Duffing+equations%22">Duffing equations</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+theory%22">Stability theory</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper employs both analytical and numerical methods to investigate the dynamic characteristics of a coupled Duffing oscillators with two-periodic excitations and distributed time delays. First, the original system is transformed to an equivalent slow-coupled system using the fast–slow analysis method. The stability of equilibrium points and the pitchfork bifurcation phenomena resulting from changes in parameters are analyzed. Specifically, the relationship between the number of coupling layers and the stable equilibrium points is explored. Subsequently, the necessary conditions for the occurrence of chaos, such as homoclinic bifurcation leading to horseshoe chaos, are derived using the Melnikov method. By integrating phase diagrams with the largest Lyapunov exponent, we analyzed the influence of various parameters on chaotic trajectories. Additionally, the specific effects of system distribution delay intensity were further illustrated through numerical simulations. [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.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1142/S021812742650029X
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 28
        StartPage: 1
    Subjects:
      – SubjectFull: Bifurcation theory
        Type: general
      – SubjectFull: Chaos theory
        Type: general
      – SubjectFull: Duffing equations
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Computer simulation
        Type: general
      – SubjectFull: Stability theory
        Type: general
    Titles:
      – TitleFull: Bifurcation and Chaos Analysis of Coupled Duffing Oscillators with Two-Periodic Excitations and Distributed Time Delays.
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            NameFull: Guo, Yu
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              M: 03
              Text: Mar2026
              Type: published
              Y: 2026
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              Value: 36
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            – TitleFull: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
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