Time Series Generation Using Nonlinear Autoregressive Model Artificial Neural Network Based Nonlinear Autoregressive Model Design for the Generation and Prediction of Lorenz Chaotic System

Abstract

This paper presents a Nonlinear Auto-Regressive (NAR) model design for the generation and prediction of Lorenz chaotic system using different Artificial Neural Network (ANN) architectures. Electroencephalogram (EEG) signals captured from brain activities demonstrate chaotic features. In order to theoretically understand brain functionalities, the dynamic chaotic time series outputs of a chaotic system with known system equations can be used to train ANN. And the ANN based NAR model can be used for the simulation and analysis of the chaotic features of brain activities. The ANN architecture design and optimization of the NAR chaotic system model is part of the preliminary research of a multidisciplinary brain research program. The ANN training results of different ANN architectures with 3 to 16 neurons in the hidden layer and 1 to 4 input delays of the NAR model, using training data generated with different step sizes provide important information for the selection of optimal training configuration to optimize the training performance. The research outcome is beneficial for the study of brain activities using EEG.