Embedding dimension estimation of chaotic time series using self-generating radial basis function network

Abstract In this paper, we apply the self-generating radial basis function network (SGRBF) to the dimension analysis of the nonlinear dynamical systems including chaotic time series. Firstly, we formulate a nonlinear time series identification problem with a nonlinear autoregressive moving average (NARMAX) model. Secondly, we propose an identification algorithm using SGRBF, which is regarded as both a three-layer network or a fuzzy model of class C ∞ with Gaussian membership function. We apply this method to the estimation of embedding dimension for chaotic time series, since the embedding dimension plays an essential role for the identification and the prediction of nonlinear dynamical systems including chaos. In this estimation method, identification problems with gradually increasing embedding dimension are solved, and the identified result is used for computing correlation coefficients between the predicted time series and the observed one. We apply this method to the embedding dimension estimation of a Henon map and a chaotic pulsation time series in a finger's capillary vessels.