Parameter joint estimation of phase space reconstruction in chaotic time series based on radial basis function neural networks

Abstract

In this paper, we propose a joint estimation method of two parameters for phase space reconstruction in chaotic time series, based on radial basis function (RBF) neural networks. And we obtain the best estimation values, according to some objective standards. Furthermore, The single-step and multi-step RBF prediction model is used to estimate the best embedding dimension and delay time, and Lorenz system is selected as an example. Finally, the estimation values are tested in the original model. The simulations show that we can obtain the best estimation values through the method, and the prediction accuracy is significantly improved.