Automatic estimation of attractor invariants

TL;DR

This paper introduces two new coarse-grained estimators for attractor invariants, specifically correlation dimension and entropy, which are robust to noise and short data lengths, and includes an automatic algorithm for their estimation.

Contribution

The paper presents novel estimators for attractor invariants and an automatic algorithm that outperforms existing methods, especially in noisy and short data scenarios.

Findings

Estimators are robust against noise and short data lengths.

The automatic algorithm accurately estimates invariants and noise level.

Outperforms similar approaches in correlation entropy estimation.

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.