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<p>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.</p>

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Chaotic dynamics of oscillators with combined elastic and dry friction nonlinearities

  • 期刊论文

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  • 发表日期：

    2026年6月2日

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  • Vladimir Bratov,
  • Sergey V. Kuznetsov

摘要

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.