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Chaotic systems with asymmetric heavy-tailed noise: Application to 3D attractors

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  • Contreras-Reyes, Javier E.

Abstract

Yilmaz et al. (Fluct. Noise Lett. 17, 1830002, 2018) investigated the stochastic phenomenological bifurcations of a generalized Chua circuit driven by Skew-Gaussian distributed noise. They proved it is possible to decrease the number of scrolls by properly choosing the stochastic excitation, manipulating the skewness and noise intensity parameters. Based on the latter, this paper proposes an extension of skew-gaussian noise based on the family of Scale Mixtures of Skew-normal (SMSN) distributions, which includes the skew-t, the skew-gaussian, and the gaussian noises as particular cases. The Lorenz, Generalized Lorenz, Proto–Lorenzand Rössler attractors driven by skew-t distributed noise are considered. Results show that the chaotic regime’s behavior is influenced by the freedom parameter degrees of skew-t noise, increasing the noise variance. This paper concludes that noise intensity increases by rescaling the skew-t distribution at zero mean, rather than by increasing the asymmetry parameter.

Suggested Citation

  • Contreras-Reyes, Javier E., 2021. "Chaotic systems with asymmetric heavy-tailed noise: Application to 3D attractors," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001727
    DOI: 10.1016/j.chaos.2021.110820
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    References listed on IDEAS

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    1. Spichak, David & Kupetsky, Audrey & Aragoneses, Andrés, 2021. "Characterizing complexity of non-invertible chaotic maps in the Shannon–Fisher information plane with ordinal patterns," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Contreras-Reyes, Javier E., 2014. "Asymptotic form of the Kullback–Leibler divergence for multivariate asymmetric heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 200-208.
    3. Yu, Simin & Tang, Wallace K.S., 2009. "Tetrapterous butterfly attractors in modified Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1740-1749.
    4. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
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    Cited by:

    1. Contreras-Reyes, Javier E., 2021. "Lerch distribution based on maximum nonsymmetric entropy principle: Application to Conway’s game of life cellular automaton," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Zhao, Tong & Li, Zhen & Deng, Yong, 2023. "Information fractal dimension of Random Permutation Set," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. Contreras-Reyes, Javier E., 2022. "Rényi entropy and divergence for VARFIMA processes based on characteristic and impulse response functions," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).

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