Nonlinear Identification and Cluster Analysis of Chaotic Attractors from a Real Implementation of Chua's Circuit

Abstract

This paper discusses the identification of nonlinear polynomial models from real data sets measured from an implementation of Chua's circuit. Data filtering issues are also discussed. The identified models are analyzed and validated and suggest that the major characteristics of the real system have been incorporated in the models. Lyapunov exponents, correlation and Lyapunov dimensions are estimated for the identified models and some practical difficulties concerning the estimation of such invariants are discussed. Cluster analysis of the identified models has been performed and it is in accord with a number of results reported in the literature. Five of the identified models are presented in the paper and because of their simple structure, it is believed that such models will be useful in the study of nonlinear dynamics of Chua's circuit.