Noise-assisted estimation of attractor invariants
| Autor: | Juan F. Restrepo, Gastón Schlotthauer |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Ingeniería de Sistemas y Comunicaciones
CORRELATION DIMENSION U CORRELATION INTEGRAL CORRELATION INTEGRAL NOISE-ASSISTED CORRELATION INTEGRAL INGENIERÍAS Y TECNOLOGÍAS purl.org/becyt/ford/2.2 [https] 01 natural sciences 010305 fluids & plasmas purl.org/becyt/ford/2 [https] 0103 physical sciences 010306 general physics Humanities CORRELATION ENTROPY Ingeniería Eléctrica Ingeniería Electrónica e Ingeniería de la Información Correlation entropy Mathematics |
| Zdroj: | CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET |
| ISSN: | 2470-0053 |
| Popis: | In this article, the noise-assisted correlation integral (NCI) is proposed. The purpose of the NCI is to estimate the invariants of a dynamical system, namely the correlation dimension (D), the correlation entropy (K2), and the noise level (σ). This correlation integral is induced by using random noise in a modified version of the correlation algorithm, i.e., the 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 of as special cases of the NCI. A third particular case is the U-correlation integral proposed herein, from which we derived coarse-grained estimators of the correlation dimension (DU m), the correlation entropy (KU m), and the noise level (σ U m ). 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 DU m and σ U m behave in a similar manner to those based on the GCI. However, for the calculation of K2, the estimator KU m outperforms its GCI-based counterpart. On the basis of 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 by using this approach, we are able to achieve statistically reliable estimations of those invariants. Fil: Restrepo Rinckoar, Juan Felipe. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Schlotthauer, Gaston. Universidad Nacional de Entre Ríos. Facultad de Ingeniería. Departamento de Matemática e Informática. Laboratorio de Señales y Dinámicas no Lineales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro de Investigaciones y Transferencia de Entre Ríos. Universidad Nacional de Entre Ríos. Centro de Investigaciones y Transferencia de Entre Ríos; Argentina |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|