State space parsimonious reconstruction of attractor produced by an electronic oscillator

Abstract

This work discusses the reconstruction, from a set of real data, of a chaotic attractor produced by a well-known electronic oscillator, Chua’s circuit. The mathematical representation used is a nonlinear differential equation of the polynomial type. One of the contributions of the present study is that structure selection techniques have been applied to help determine the regressors in the model. Models of the chaotic attractor obtained with and without structure selection were compared. The main differences between structure-selected models and complete structure models are: i) the former are more parsimonious that the latter, ii) fixed-point symmetry is guaranteed for the former, iii) for structure-selected models a trivial fixed point is also guaranteed, and iv) the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models.