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Universal BHP distribution and nonlinear prediction in complex systems using the Ruelle-Takens embedding

Congress: 2008
Author(s): Rui Gonçalves, A. A. Pinto

Keyword(s): Nonlinear dynamics, Ruelle- Takens embedding, BHP distribution, river flow prediction
AbstractWe exploit ideas of nonlinear dynamics and statistical physics in a complex non-deterministic dynamical setting. Our object of study is the observed riverflow time series of the Portuguese Paiva river whose water is used for public supply. The Ruelle- Takens delay embedding of the daily riverflow time series revealed an intermittent dynamical behavior due to precipitation occurrence. The laminar phase occurs in the absence of rainfall. The nearest neighbor method of prediction revealed good predictability in the laminar regime, but we warn that this method is misleading in the presence of rain. We present some new insights between the quality of the prediction in the laminar regime, the embedding dimension, and the number of nearest neighbors considered. After this careful study of the laminar phase, we find, unexpectedly, that the BHP distribution is an approximation of the empirical distribution of the relative decay. Furthermore, the empirical distribution of the relative decay computed using the nearest neighbors predictor is even closer to the BHP distribution. Hence, the nearest neighbor method of prediction acts as a filter which does not eliminate the randomness but exhibits its main character in the laminar regime.
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