Dynamical Disorder and Self-Correlation in the Characterization of Nonlinear Systems. Application to Deterministic Chaos.

Hernández Álvarez, Juan Antonio and Benito Zafrilla, Rosa Maria and Losada González, Jose Carlos (2011). Dynamical Disorder and Self-Correlation in the Characterization of Nonlinear Systems. Application to Deterministic Chaos.. "International Journal of Bifurcation and Chaos", v. 21 (n. 3); pp. 963-983. ISSN 0218-1274. https://doi.org/10.1142/S0218127411028805.

Description

Title: Dynamical Disorder and Self-Correlation in the Characterization of Nonlinear Systems. Application to Deterministic Chaos.
Author/s:
  • Hernández Álvarez, Juan Antonio
  • Benito Zafrilla, Rosa Maria
  • Losada González, Jose Carlos
Item Type: Article
Título de Revista/Publicación: International Journal of Bifurcation and Chaos
Date: March 2011
ISSN: 0218-1274
Volume: 21
Subjects:
Faculty: E.T.S.I. Agrónomos (UPM) [antigua denominación]
Department: Física y Mecánica Fundamental, Aplicada a la Ingeniería Agroforestal [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

A new methodology to characterize nonlinear systems is described. It is based on the measurement over the time series of two quantities: the "Dynamical order" and the "Self-correlation". The averaged "Scalar" and "Perpendicular" products are introduced to measure these quantities. While this approach can be applied to general nonlinear systems, the aim of this work is to focus on the characterization and modeling of chaotic systems. In order to illustrate the method, applications to a two-dimensional chaotic system and the modeling of real telephony traffic series are presented. Three important aspects are discussed: the use of the averaged "Scalar" product as supplement of the "Lyapunov exponent", the use of the averaged "Perpendicular" product as a refinement of the "Mutual information" and the reduction of m-dimensional systems to the study of only one dimension. This new conceptual framework introduces a perspective to characterize real and theoretical processes with a unifying method, irrespective of the system classification.

More information

Item ID: 7095
DC Identifier: http://oa.upm.es/7095/
OAI Identifier: oai:oa.upm.es:7095
DOI: 10.1142/S0218127411028805
Official URL: http://www.worldscinet.com/ijbc/21/2103/S0218127411028805.html
Deposited by: Memoria Investigacion
Deposited on: 24 May 2011 10:19
Last Modified: 20 Apr 2016 16:12
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