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Correlation Dimension for Two Experimental Time Series

Content Provider	Springer Nature Link
Author	Celletti, A. Bajo Lorenzana, V. M. Villa, A. E. P.
Copyright Year	1998
Abstract	. A method for detecting the dimension of a dynamical system encompassing simultaneously two distinct discrete time series is presented. The time series are provided by the same observable taking distinct and independent initial conditions or they can be formed by realizations of different observables measured simultaneously in a symmetric attractor. The method is derived from an extension of the technique introduced in [18, 19] for single time series and allows to evaluate the common correlation dimension of the chaotic attractor. The correlation dimension associated to two time series is computed for some mathematical models. In particular the two-dimensional standard mapping is analysed; a dissipative four-dimensional Hénon-like mapping is introduced and analyses with single and multiple time series are performed. The double series method provides a more accurate and efficient evaluation of the embedding and correlation dimensions in all experimental cases. The method is also applied to discrete time series derived from multiple single unit electrophysiological recordings. Several examples of significant dynamics have been revealed. The results are confirmed by the computation of the (double series) entropy and compared to usual time domain analyses performed in Neuroscience. The double series method is proposed as a complementary method for investigation of dynamical properties of cell assemblies and its potential usefulness for detecting higher order cognitive processes is discussed.Sommario: Si presenta un metodo per determinare la dimensione di un sistema dinamico comprendente simultaneamente due diverse serie temporali discrete. Le serie temporali sono costituite dallo stesso osservabile, prendendo condizioni iniziali distinte e indipendenti, oppure sono formate da realizzazioni di differenti osservabili misurati simultaneamente in un attrattore simmetrico. Il metodo deriva da un'estensione della tecnica introdotta in [18,19] per singole serie temporali e consente di valutare la comune dimensione di correlazione dell'attrattore caotico. La dimensione di correlazione associata a due serie temporali è calcolata per alcuni modelli matematici. In particolare si analizza la mappa standard bidimensionale; si introduce inoltre una mappa a 4 dimensioni analoga alla mappa di Hénon si analizzano serie temporali singole e multiple. Il metodo delle serie multiple consente una valutazione più accurata ed efficiente delle dimensioni di immersione e di correlazione nei casi sperimentali. Si applica inoltre il metodo a serie discrete associate a registrazioni elettrofisiologiche. Sono stati determinati svariati esempi di dinamica significativa. I risultati sono confermati dal calcolo dell'entropia con il metodo delle doppie serie e sono stati confrontati con le analisi standard che si utilizzano nel campo delle Neuroscienze. Si propone il metodo della doppia serie come uno strumento complementare per lo studio delle proprietà dinamiche di gruppi di cellule e per l'analisi di processi cognitivi.
Starting Page	381
Ending Page	396
Page Count	16
File Format	PDF
ISSN	00256455
Journal	Meccanica
Volume Number	33
Issue Number	4
e-ISSN	15729648
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	1998-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Mechanics Mechanical Engineering Automotive and Aerospace Engineering, Traffic Civil Engineering
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Condensed Matter Physics Mechanical Engineering

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