Noise-assisted estimation of attractor invariants

JUAN FELIPE RESTREPO; GASTÓN SCHLOTTHAUER

Physical Review E

American Physical Society

Lugar: Washington DC; Año: 2016 vol. 94

In this article the noise-assisted correlation integral (NCI) is proposed, aimed to estimate the invariants of a dynamical system: correlation dimension (D), correlation entropy (K2), and noise level (sigma). This correlation integral is induced by the use of random noise in a modied version of the correlation algorithm: noise-assisted correlation algorithm. We demonstrate how the correlation integral by Grassberger et al. and the Gaussian kernel correlation integral (GCI) by Diks can be thought as special cases of the NCI. A third particular case is the U-correlation integral (UCI) here proposed, from which we derived coarse-grained estimators of correlation dimension (D^U_m), correlation entropy (K^U_m), and noise level (sigma^U_m ). Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under dierent noise conditions and data lengths. The results show that the estimators D^U_m and sigma^U_m behave in a similar manner to those based on the GCI. However, for the calculation of K2 the estimator K^U_m outperforms its GCI based counterpart. Supported on the behavior of these estimators we have proposed an automatic algorithm to find D, K2 and sigma from a given time series. The results show that this approach is able to achieve statistically reliable estimations of those invariant.