A neural-based method for choosing embedding dimension in chaotic time series analysis

Abstract

This paper introduces applying a neural-based method for determining minimum embedding dimension for chaotic time series analysis. Many methods have been proposed on selecting optimal values for delay embedding parameters. Some frequently used methods are investigated and practically implemented, and then by using artificial neural networks (ANN) as one of components of the computational intelligence (CI) an approach was proposed to determine the minimum embedding dimension. This approach benefits from the multilayer feedforward neural networks ability in function approximation. The advantage of this method is that it gives a global nonlinear model for the system that can be used for many purposes such as prediction, noise reduction and control. Based on the achieved neural model an indirect algorithm for maximal Lyapunov estimation was suggested.