Statistical methods in nonlinear dynamics

Pramana

R Harish²  S V M Satyanarayana¹  K P N Murthy1³ 

[1] Health and Safety Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India$$;Reactor Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India$$;Materials Science Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603 102, India$$

关键词: Statistical methods;    nonlinear dynamics;    chaos;    Lyapunov exponents;    power spectrum;    extreme value statistics.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

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.

【 授权许可】

Unknown