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Statistical methods in nonlinear dynamics

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Abstract

Sensitivity to initial conditions in nonlinear dynamical systems leads to exponential divergence of trajectories that are initially arbitrarily close, and hence to unpredictability. Statistical methods have been found to be helpful in extracting useful information about such systems. In this paper, we review briefly some statistical methods employed in the study of deterministic and stochastic dynamical systems. These include power spectral analysis and aliasing, extreme value statistics and order statistics, recurrence time statistics, the characterization of intermittency in the Sinai disorder problem, random walk analysis of diffusion in the chaotic pendulum, and long-range correlations in stochastic sequences of symbols.

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Authors and Affiliations

  1. Materials Science Division, Indira Gandhi Centre for Atomic Research, 603 102, Kalpakkam, India

    K. P. N Murthy

  2. Reactor Physics Division, Indira Gandhi Centre for Atomic Research, 603 102, Kalpakkam, India

    R. Harish

  3. Health and Safety Division, Indira Gandhi Centre for Atomic Research, 603 102, Kalpakkam, India

    S. V. M. Satyanarayana

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  1. K. P. N Murthy
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  2. R. Harish
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  3. S. V. M. Satyanarayana
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Murthy, K.P.N., Harish, R. & Satyanarayana, S.V.M. Statistical methods in nonlinear dynamics. Pramana - J Phys 64, 353–370 (2005). https://doi.org/10.1007/BF02704563

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