Identification and prediction of discrete chaotic maps applying a Chebyshev neural network

A new approach to reconstructing and predicting discrete chaotic maps is developed. It is based on the feed-forward neural network which decomposes the analyzed chaotic map in orthogonal Chebyshev polynomials. We show that the Chebyshev neural network (CNN) significantly exceeds the traditional multi-layer perceptron (MLP) in learning rate and in the accuracy of approximating an unknown map.