Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2000-11-09
Nonlinear Sciences
Chaotic Dynamics
4 pages, 2 figures, RevTeX V4b4, submitted to Phys. Rev. Lett
Scientific paper
10.1016/S0375-9601(01)00128-1
In the analysis of time series from nonlinear sources, mutual information (MI) is used as a nonlinear statistical criterion for the selection of an appropriate time delay in time delay reconstruction of the state space. MI is a statistic over the sets of sequences associated with the dynamical source, and we examine here the distribution of MI, thus going beyond the familiar analysis of its average alone. We give for the first time the distribution of MI for a standard, classical communications channel with Gaussian, additive white noise. For time series analysis of a dynamical system, we show how to determine the distribution of MI and discuss the implications for the use of average mutual information (AMI) in selecting time delays in phase space reconstruction.
Abarbanel Henry D. I.
Masuda Naoki
Rabinovich Mikhail I.
Tumer Evren
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