Distinguishing Noise from Chaos

O. A. Rosso, H. A. Larrondo, M. T. Martin, A. Plastino, and M. A. Fuentes
Phys. Rev. Lett. 99, 154102 – Published 12 October 2007

Abstract

Chaotic systems share with stochastic processes several properties that make them almost undistinguishable. In this communication we introduce a representation space, to be called the complexity-entropy causality plane. Its horizontal and vertical axis are suitable functionals of the pertinent probability distribution, namely, the entropy of the system and an appropriate statistical complexity measure, respectively. These two functionals are evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the system. Several well-known model-generated time series, usually regarded as being of either stochastic or chaotic nature, are analyzed so as to illustrate the approach. The main achievement of this communication is the possibility of clearly distinguishing between them in our representation space, something that is rather difficult otherwise.

  • Figure
  • Received 15 June 2007

DOI:https://doi.org/10.1103/PhysRevLett.99.154102

©2007 American Physical Society

Authors & Affiliations

O. A. Rosso1,2, H. A. Larrondo3, M. T. Martin4, A. Plastino4, and M. A. Fuentes5,6

  • 1Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan NSW 2308, Australia
  • 2Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Ciudad Universitaria, Buenos Aires, Argentina
  • 3Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Juan B. Justo 4302, 7600 Mar del Plata, Argentina
  • 4Instituto de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 727, 1900 La Plata, Argentina
  • 5Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA
  • 6Instituto Balseiro, Centro Atómico Bariloche and CONICET, 8400 Bariloche, Argentina

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Issue

Vol. 99, Iss. 15 — 12 October 2007

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