Publication | Closed Access
Theory of Diffusion and Intermittency in Chaotic Systems. III: New Approach to Temporal Correlations
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1987
Year
Fourier TransformMoment MtDeterministic Dynamical SystemChaos TheoryEntropyHigh-dimensional ChaosNew ApproachTemporal CorrelationsChaotic SystemsNeuroscienceNew Statistical-mechanical ApproachChaotic MixingNonlinear Time Series
A new statistical-mechanical approach to the temporal correlation in one-dimensional time series {ut; 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 Mt(q) ≡≪exp (qtzt) >, where zt≡t-1Σt-1j=0uj is the scale-dependent average and the parameter q is real. The temporal correlations turn out to be specified with sets of characteristic frequencies {ωq} and line widths {γq} . It is shown that the conventional double-time correlation function theory deals only with the limit q →0. Furthermore we will find that {ωq} and {γq} generally depend on q. This implies that different characteristic dynamics embedded in {ut} , 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.