RECOGNITION OF CHAOTIC TIME-SERIES USING A PARAMETRIZED FAMILY OF NONLINEAR PREDICTORS

For several chaotic time series recorded from a dynamical system with different bifurcation parameter values, Kajiwara and colleagues propos ed a method (bifurcation diagram reconstruction) of reconstructing a p arametrized family of nonlinear predictors which exhibits bifurcation phenomena qualitatively similar to the original [9, 10]. Based on this method, chaotic time series can be characterized by the parameter val ues of the nonlinear predictors. We call the characterization of chaot ic time series in terms of the underlying bifurcation parameter values ''recognition'' of chaotic time series. In order to apply the idea to real-world systems, which are usually described by a continuous-time dynamical system and also contain observational noise, several extensi ons of the method are necessary. Hence, this paper presents an extende d algorithm for reconstructing bifurcation diagrams of a continuous-ti me dynamical system in the presence of observational noise. The effect iveness of the method is demonstrated by a numerical experiment using the Rossler equation. Applicability of the bifurcation diagram reconst ruction technique to the recognition of chaotic time series is also ex amined. (C) 1998 Scripta Technica.