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Chaotic dynamics of oscillators with combined elastic and dry friction nonlinearities.

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Title: Chaotic dynamics of oscillators with combined elastic and dry friction nonlinearities.
Authors: Bratov, Vladimir1 (AUTHOR) v.bratov@napier.ac.uk, Kuznetsov, Sergey V.2 (AUTHOR) kuzn-sergey@yandex.ru
Source: Zeitschrift für Angewandte Mathematik und Physik (ZAMP). Jun2026, Vol. 77 Issue 6, p1-16. 16p.
Subjects: Duffing equations, Dry friction, Chaos theory, Harmonic oscillators, Poincare maps (Mathematics), Bifurcation diagrams, Friction
Abstract: The forced harmonic oscillator with combined Duffing cubic stiffness and Bliman–Sorine friction is analyzed using Poincaré sections and parameter space basins of attraction, constructed as functions of two key oscillator parameters: friction stiffness and forcing amplitude. The analysis uncovers several key dynamical features: (1) Chaotic behavior is absent when the cubic stiffness term vanishes; (2) chaotic regimes emerge as soon as the cubic stiffness becomes nonzero; (3) the parameter space develops strongly entangled basins, reflecting extreme sensitivity of attractor selection to frictional micro-mechanics; and (4) variations in the Bliman–Sorine parameters induce pronounced topological changes in bifurcation diagrams. These findings provide new insight into the structure of oscillations in systems governed by the Bliman–Sorine friction model. Numerical simulations are performed using a variable-step Adams–Bashforth–Moulton explicit–implicit scheme to ensure reliable long-time integration. [ABSTRACT FROM AUTHOR]
Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature 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.)
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  Data: Chaotic dynamics of oscillators with combined elastic and dry friction nonlinearities.
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  Data: <searchLink fieldCode="AR" term="%22Bratov%2C+Vladimir%22">Bratov, Vladimir</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> v.bratov@napier.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Kuznetsov%2C+Sergey+V%2E%22">Kuznetsov, Sergey V.</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> kuzn-sergey@yandex.ru</i>
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  Data: <searchLink fieldCode="DE" term="%22Duffing+equations%22">Duffing equations</searchLink><br /><searchLink fieldCode="DE" term="%22Dry+friction%22">Dry friction</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Harmonic+oscillators%22">Harmonic oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Poincare+maps+%28Mathematics%29%22">Poincare maps (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+diagrams%22">Bifurcation diagrams</searchLink><br /><searchLink fieldCode="DE" term="%22Friction%22">Friction</searchLink>
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  Data: The forced harmonic oscillator with combined Duffing cubic stiffness and Bliman–Sorine friction is analyzed using Poincaré sections and parameter space basins of attraction, constructed as functions of two key oscillator parameters: friction stiffness and forcing amplitude. The analysis uncovers several key dynamical features: (1) Chaotic behavior is absent when the cubic stiffness term vanishes; (2) chaotic regimes emerge as soon as the cubic stiffness becomes nonzero; (3) the parameter space develops strongly entangled basins, reflecting extreme sensitivity of attractor selection to frictional micro-mechanics; and (4) variations in the Bliman–Sorine parameters induce pronounced topological changes in bifurcation diagrams. These findings provide new insight into the structure of oscillations in systems governed by the Bliman–Sorine friction model. Numerical simulations are performed using a variable-step Adams–Bashforth–Moulton explicit–implicit scheme to ensure reliable long-time integration. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Zeitschrift für Angewandte Mathematik und Physik (ZAMP) is the property of Springer Nature 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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        Value: 10.1007/s00033-026-02826-5
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      – Code: eng
        Text: English
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      – SubjectFull: Duffing equations
        Type: general
      – SubjectFull: Dry friction
        Type: general
      – SubjectFull: Chaos theory
        Type: general
      – SubjectFull: Harmonic oscillators
        Type: general
      – SubjectFull: Poincare maps (Mathematics)
        Type: general
      – SubjectFull: Bifurcation diagrams
        Type: general
      – SubjectFull: Friction
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      – TitleFull: Chaotic dynamics of oscillators with combined elastic and dry friction nonlinearities.
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              M: 06
              Text: Jun2026
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              Y: 2026
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