Invited Symposium: Nonlinear Dynamical Systems in Psychiatry
The results concerning the Sugihara & May algorithm suggest that the observed time series are non random, nonlinear and deterministic, because the correlation between actual and predicted data decreases as the prediction time increases (Fig.3).
Fig.3 : Nonlinear forecasts (Sugihara & May, 1990) for prediction times varying from 1 to 12 (X-axis) and embedding dimensions varying from 2 to 4 (Z-axis), corresponding to each time series (full lines). Correlation coefficients are on the Y-axis. As a validation, results obtained with one surrogate data built from each time series are also depicted (dot lines).
As depicted on Fig. 4, the results obtained with the ‘Noise Versus Chaos’ algorithm of Kennel & Isabelle confirm the previous results, because the prediction errors of the actual time series are significantly lower than those of the surrogates. Both results support the hypothesis of deterministic chaos characterizing the dynamics of the activity bouts.
Fig. 4 . 'Noise versus Chaos' test (Kennel & Isabelle algorithm, 1992). Comparison of the prediction errors between the actual data and a set of 30 surrogate data. Z scores for each actual time series (top). The horizontal line corresponds to the level of significance. As a validation, results obtained with one surrogate data built from each time series are also depicted (bottom).
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|Guillot, A.; Meyer, J.A.; (1998). A Dynamical Analysis of Action Selection in the Laboratory Mouse. Presented at INABIS '98 - 5th Internet World Congress on Biomedical Sciences at McMaster University, Canada, Dec 7-16th. Invited Symposium. Available at URL http://www.mcmaster.ca/inabis98/sulis/guillot0208/index.html|
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