Predicting chaotic time series and replicating chaotic attractors based on two novel echo state network models

Abstract

Neural network is the inevitable outcome of the rapid development of artificial intelligence. Based on the idea of homotopy and combined activation function, two novel echo state network (ESN) models are proposed. Compared with several activation functions commonly used in the neural network, the proposed models provide intuitive but effective approaches to chaotic forecasting, and the prediction accuracy is higher. Secondly, for the Mackey-Glass (MG) time series and Rössler attractor, the prediction errors and prediction step sizes of the two novel models are superior to many pre-existing ESN models, which demonstrates the merit of the proposed models. Moreover, several parameters play key roles in network training, such as spectral radius, sparse degree etc., and their effects on network performance are analyzed. Notably, it is also investigated that the trained network can replicate Rössler chaotic attractor well. At the end of the results, the parameters of the proposed models are optimized, and the relatively optimized parameters are obtained after a large number of data experiments.