Identification of discrete chaotic maps with singular points

We investigate the ability of artificial neural networks to reconstruct dis crete chaotic maps with singular points. We use as a simple test model the Cusp map. We compare the traditional Multilayer Perceptron, the Chebyshev N eural 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 determinati on of the singular point we are able to accurately approximate discrete cha otic maps with singularities.