Prog. Theor. Phys. Vol. 78 No. 2 (1987) pp. 268-281

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Theory of Diffusion and Intermittency in Chaotic Systems. III

— New Approach to Temporal Correlations —

Hirokazu Fujisaka and Masayoshi Inoue

Department of Physics, Kagoshima University, Kagoshima 890

(Received March 26, 1987)

Abstract:

A new statistical-mechanical approach to the temporal correlation in one-dimensional time series { u_t; t=0,1,2,3, \dotsb} generated by a chaotic dynamics is developed. This is done by studying poles of the Fourier transform of the moment M_t(q) ≡<exp (qtz_t) >, where z_t≡t^-1Σ^t-1_j=0 u_j is the scale-dependent average and the parameter q is real. The temporal correlations turn out to be specified with sets of characteristic frequencies { ω_q } and line widths { γ_q } . It is shown that the conventional double-time correlation function theory deals only with the limit q →0. Furthermore we will find that { ω_q } and { γ_q } generally depend on q. This implies that different characteristic dynamics embedded in { u_t } , including motions which can be never described by the double-time correlation function approach, are able to be singled out in a unified way by controlling the parameter q.

URL : http://ptp.ipap.jp/link?PTP/78/268/
DOI : 10.1143/PTP.78.268

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Citing Article(s) :

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Global Bifurcations and Fluctuation Spectra of Local Expansion Rates in Nonlinear Dynamical Systems

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