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Detection of the chaotic behaviour of a bouncing ball by the 0–1 test

Author

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  • Litak, G.
  • Syta, A.
  • Budhraja, M.
  • Saha, L.M.

Abstract

We examine the two-dimensional map of a bouncing ball system. To distinguish between periodic and chaotic solutions we propose the 0–1 test. This method is based on the spectral properties of chaotic system quantifying the system response: 0 for the regular and 1 for the chaotic solution. The obtained results have been confirmed by the calculation of the maximal Lyapunov exponent defined by the product of Jacobian matrices calculated along corresponding trajectories.

Suggested Citation

  • Litak, G. & Syta, A. & Budhraja, M. & Saha, L.M., 2009. "Detection of the chaotic behaviour of a bouncing ball by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1511-1517.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1511-1517
    DOI: 10.1016/j.chaos.2009.03.048
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    References listed on IDEAS

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    1. Syta, Arkadiusz & Litak, Grzegorz, 2008. "Stochastic description of the deterministic Ricker’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 262-268.
    2. P. Gaspard & M. E. Briggs & M. K. Francis & J. V. Sengers & R. W. Gammon & J. R. Dorfman & R. V. Calabrese, 1998. "Experimental evidence for microscopic chaos," Nature, Nature, vol. 394(6696), pages 865-868, August.
    3. Litak, Grzegorz & Syta, Arkadiusz & Wiercigroch, Marian, 2009. "Identification of chaos in a cutting process by the 0–1 test," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2095-2101.
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    Cited by:

    1. Ding, Shun-Liang & Song, En-Zhe & Yang, Li-Ping & Litak, Grzegorz & Yao, Chong & Ma, Xiu-Zhen, 2016. "Investigation on nonlinear dynamic characteristics of combustion instability in the lean-burn premixed natural gas engine," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 99-110.
    2. Belaire-Franch, Jorge, 2020. "The finite sample behavior of the 0–1 test for chaos," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    3. Ekassi, E.L. Nnomo & Foupouapouognigni, O. & Siewe, M. Siewe, 2024. "Nonlinear dynamics and Gaussian white noise excitation effects in a model of flow-induced oscillations of circular cylinder," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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