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Estimation of the Largest Lyapunov Exponent for a Model of Cross-Shaped Waves in a Rectangular Channel of Finite Size

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The largest Lyapunov exponent characterizes the degree of exponential divergence of close trajectories of a dynamical system. The presence of a positive Lyapunov exponent in the system reveals rapid divergence of any two arbitrarily close trajectories with time and sensitivity to the values of the initial conditions. Therefore, as a result of determination of the Lyapunov exponent, it becomes possible to identify the system in a sense of chaotic dynamics. We propose a method for increasing the accuracy of the Benettin numerical algorithm aimed at the evaluation of the largest Lyapunov exponent in the case of a dissipative dynamical system. The results of calculations are presented for the hydrodynamic model of cross-shaped waves in a rectangular channel of finite size.

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Authors and Affiliations

  1. Kyiv National University of Construction and Architecture, Kyiv, Ukraine

    V. D. Pechuk

  2. Institute of Hydromechanics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    T. S. Krasnopolska

Authors
  1. V. D. Pechuk
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  2. T. S. Krasnopolska
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Correspondence to T. S. Krasnopolska.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 65, No. 1-2, pp. 209–215, January–June, 2022.

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Pechuk, V.D., Krasnopolska, T.S. Estimation of the Largest Lyapunov Exponent for a Model of Cross-Shaped Waves in a Rectangular Channel of Finite Size. J Math Sci 282, 862–869 (2024). https://doi.org/10.1007/s10958-024-07221-x

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