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Computational Intelligence and Neuroscience
Volume 2015, Article ID 145874, 10 pages
Research Article

Impact of Noise on a Dynamical System: Prediction and Uncertainties from a Swarm-Optimized Neural Network

Departamento de Física y Astronomía, Universidad de La Serena, Casilla 554, La Serena, Chile

Received 27 April 2015; Revised 15 July 2015; Accepted 27 July 2015

Academic Editor: Saeid Sanei

Copyright © 2015 C. H. López-Caraballo et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term . The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level from 0.01 to 0.1.