Noise-assisted estimation of attractors' invariants

JUAN FELIPE RESTREPO; GASTÓN SCHLOTTHAUER

PHYSICAL REVIEW E

AMER PHYSICAL SOC

Lugar: New York; Año: 2016 vol. 94 p. 12212 - 12231

1539-3755

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 noiselevel (σ). This correlation integral is induced by the use of random noise in a modified version of the correlation algorithm: noise-assisted correlation algorithm. We demonstrate how the correlationintegral 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 (DmU), correlation entropy (KmU), and noise level (σmU), Using time series from the Henon map and the Mackey-Glass system, we analyze the behavior of these estimators under different noise conditions and data lengths. The results show that the estimators DmU and σmU behave in a similar manner to those based on the GCI. However, for the calculation of K2 the estimator KmU outperforms its GCI based counterpart. Supported on the behavior of these estimators we have proposed an automatic algorithm to find D, K2 and σ from a given time series. The results show that this approach is able to achieve statistically reliable estimations of those invariant.