Recognition of chaotic time series using a parametrized family of nonlinear predictors

Abstract

For several chaotic time series recorded from a dynamical system with different bifurcation parameter values, Kajiwara and colleagues proposed a method (bifurcation diagram reconstruction) of reconstructing a parametrized 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 values of the nonlinear predictors. We call the characterization of chaotic 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 extensions of the method are necessary. Hence, this paper presents an extended algorithm for reconstructing bifurcation diagrams of a continuous-time dynamical system in the presence of observational noise. The effectiveness of the method is demonstrated by a numerical experiment using the Rössler equation. Applicability of the bifurcation diagram reconstruction technique to the recognition of chaotic time series is also examined. © 1998 Scripta Technica. Electron Comm Jpn Pt 3, 81(3): 35–46, 1998