Statistical methods in nonlinear dynamics

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,...

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Published inPramāṇa Vol. 64; no. 3; pp. 353 - 370
Main Authors Murthy, K. P. N, Harish, R., Satyanarayana, S. V. M.
Format Journal Article
LanguageEnglish
Published 01.03.2005
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Summary: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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
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ISSN:0304-4289
0973-7111
DOI:10.1007/BF02704563