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. Akishin,1 P. Akritas,2,3 I. Antoniou,2,3 and V. V. Ivanov1,2

 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
3Theoretische Natuurkunde, Free University of Brussels, Brussels, Belgium
Received 22 September 2000

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.