USING SOME RECENT TECHNIQUES FROM CHAOS THEORY TO ANALYZE TIME-SERIES IN ECOLOGY

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Abstract
Extraction of the underlying dynamics of large biological systems is a crucial step to understanding their mechanisms and predicting their future behaviors. Some of the techniques developed in physics to analyze chaotical phenomena should be applied with caution when the data are short and noisy. In this paper, we compared the Eckmann-Ruelle Linearization (ERL) local prediction method, and Neural Network (NN), fitting of a global nonlinear function, in the context of population dynamics. Data were generated by a discrete model and subjected to measurement noise. Prediction errors were analyzed according to noise level and length of the observations, using the above two methods Where the noise level is high, ERL is more effective for prediction than NN. On the basis of these results, we proposed for short series of available observations, that additional data be generated by the Eckmann—Ruelle linearization method and these data be used as input for Neural Nets in order to obtain a global function for the observed dynamics. This gave more reliable results than when we apply the NN method directly . Two examples are given, in ecology and epidemiology.

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