Prediction of the chaotic time series from parameter-varying systems using artificial neural networks

Prediction of the chaotic time series generated by the complex parameter-varying systems is researched in this paper. The parameter-varying Logistic system is constructed firstly, and the properties of this kind of system are analyzed. These systems, whose parameter values change with time, do not have attractor shape invariable with time evolution because of their continually changing dynamical property. Combining the Takens' embedding theorem and the artificial neural networks (ANN) theory, we interprete the feasible reason that ANN method can be used to predict the chaos systems with the invariable attractor shape, and then discuss the potential problem that will be met when using ANN to predict the parameter-varying system. Experiments of forecasting the chaotic time series from parameter-varying Ikeda system using neural networks have been performed. The previous theoretical analyses are validated by the experiment results. The results also show that if only simply increasing the training data, the neural networks' predicting generalization ability may be reduced, the generalized predicting result on the parameter-varying system is especially seriously affected by the selected training data set. So prediction of the parameter-varying systems must be well resolved before the chaotic time series prediction can be made practical.