Identification of discrete chaotic maps with singular points (Q5953847)

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.