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Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems

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  • Andrzej Stefanski
  • Tomasz kapitaniak

Abstract

We describe the method of estimation of the largest Lyapunov exponent of nonsmooth dynamical systems using the properties of chaos synchronization. The method is based on the coupling of two identical dynamical systems and is tested on two examples of Duffing oscillator: (i) with added dry friction, (ii) with impacts.

Suggested Citation

  • Andrzej Stefanski & Tomasz kapitaniak, 2000. "Using chaos synchronization to estimate the largest lyapunov exponent of nonsmooth systems," Discrete Dynamics in Nature and Society, Hindawi, vol. 4, pages 1-9, January.
    • Handle: RePEc:hin:jnddns:968905
    DOI: 10.1155/S1026022600000200
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    Cited by:

    1. Panahi, Shirin & Nazarimehr, Fahimeh & Jafari, Sajad & Sprott, Julien C. & Perc, Matjaž & Repnik, Robert, 2021. "Optimal synchronization of circulant and non-circulant oscillators," Applied Mathematics and Computation, Elsevier, vol. 394(C).
    2. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "C-oscillators and stability of stationary cluster structures in lattices of diffusively coupled oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 686-701.
    3. Stefanski, Andrzej & Dabrowski, Artur & Kapitaniak, Tomasz, 2005. "Evaluation of the largest Lyapunov exponent in dynamical systems with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1651-1659.
    4. Verichev, Nikolai N. & Verichev, Stanislav N. & Wiercigroch, Marian, 2009. "Asymptotic theory of chaotic synchronization for dissipative-coupled dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 752-763.
    5. Li, Hang & Shen, Yongjun & Han, Yanjun & Dong, Jinlu & Li, Jian, 2023. "Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    6. Borys, Przemyslaw & Grzywna, Zbigniew J., 2006. "Diffusion as a result of transition in behavior of deterministic maps," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 156-165.

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