Identification of discrete chaotic maps with singular points. Issue 3 (2001)

• Record Type: Journal Article
• Authors: Akishin, P. G.; Akritas, P.; Antoniou, I.; Ivanov, V. V.
• Is Part Of: Discrete dynamics in nature and society. Volume 6:Issue 3(2001)
• Page Start: 147
• Page End: 156
• Publication Date: 2001
• Subjects: Neural networks; Chaotic maps; Wavelets; System analysis -- Periodicals; Dynamics -- Periodicals; Chaotic behavior in systems -- Periodicals; Differentiable dynamical systems -- Periodicals; 003.05
• DOI: 10.1155/S1026022601000164
• Languages: English
• ISSNs: 1026-0226

Abstract

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.