Automatic estimation of attractor invariants

Abstract

The invariants of an attractor have been the most used resource to characterize a nonlinear dynamics. Their estimation is a challenging endeavor in short-time series and/or in presence of noise. In this article, we present two new coarse-grained estimators for the correlation dimension and for the correlation entropy. They can be easily estimated from the calculation of two U-correlation integrals. We have also developed an algorithm that is able to automatically obtain these invariants and the noise level in order to process large data sets. This method has been statistically tested through simulations in low-dimensional systems. The results show that it is robust in presence of noise and short data lengths. In comparison with similar approaches, our algorithm outperforms the estimation of the correlation entropy.