Identification of Discrete Chaotic Maps with Singular Points

We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the...

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Bibliographic Details
Published in:Discrete Dynamics in Nature and Society 2001-01, Vol.2001 (3), p.147-156
Main Authors: Akishin, P. G., Akritas, P., Antoniou, I., Ivanov, V. V.
Format: Article
Language:English
Subjects:
Neural networks
Chaotic maps
Wavelets
Online Access:Get full text
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Summary:We investigate the ability of artificial neural networks to reconstruct discrete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev Neural Network and the Wavelet Neural Network. The numerical scheme for the accurate determination of a singular point is also developed. We show that combining a neural network with the numerical algorithm for the determination of the singular point we are able to accurately approximate discrete chaotic maps with singularities.
ISSN:1026-0226
1607-887X
DOI:10.1155/S1026022601000164