Discrete Dynamics in Nature and Society
Volume 6 (2001), Issue 3, Pages 147-156
doi:10.1155/S1026022601000164
Identification of discrete chaotic maps with singular points
P.G. Akishin1
, P. Akritas2
, I. Antoniou2
and V.V. Ivanov1
1Laboratory of Computing Techniques and Automation, Joint Institute for Nuclear Research, Dubna 141980, Russia
2lnternational Solvay Institute for Physics and Chemistry, CP-231, ULB, Campus Plaine, Bd. du Triomphe, Brussels 1050, Belgium
Abstract
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.