Eur. Phys. J. B 69, 37-43 (2009)
https://doi.org/10.1140/epjb/e2009-00146-y

Detecting and quantifying temporal correlations in stochastic resonance via information theory measures

¹ Centre for Bioinformatics, Biomarker Discovery and Information-Based Medicine and Hunter Medical Research Institute, School of Electrical Engineering and Computer Science, The University of Newcastle, University Drive, Callaghan, NSW, 2308, Australia
² Instituto de Cálculo, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1428 Ciudad Universitaria, Buenos Aires, Argentina
³ Departament de Fisica i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Colom 11, Terrassa 08222, Barcelona, Spain

Corresponding author: ^a cris@fisica.edu.uy

Received: 20 January 2009
Revised: 1 April 2009
Published online: 29 April 2009

Abstract

We show that Information Theory quantifiers are suitable tools for detecting and for quantifying noise-induced temporal correlations in stochastic resonance phenomena. We use the Bandt & Pompe (BP) method [Phys. Rev. Lett. 88, 174102 (2002)] to define a probability distribution, P, that fully characterizes temporal correlations. The BP method is based on a comparison of neighboring values, and here is applied to the temporal sequence of residence-time intervals generated by the paradigmatic model of a Brownian particle in a sinusoidally modulated bistable potential. The probability distribution P generated via the BP method has associated a normalized Shannon entropy, H[P], and a statistical complexity measure, C[P], which is defined as proposed by Rosso et al. [Phys. Rev. Lett. 99, 154102 (2007)]. The statistical complexity quantifies not only randomness but also the presence of correlational structures, the two extreme circumstances of maximum knowledge (“perfect order") and maximum ignorance (“complete randomness") being regarded an “trivial", and in consequence, having complexity C = 0. We show that both, H and C, display resonant features as a function of the noise intensity, i.e., for an optimal level of noise the entropy displays a minimum and the complexity, a maximum. This resonant behavior indicates noise-enhanced temporal correlations in the sequence of residence-time intervals. The methodology proposed here has great potential for the precise detection of subtle signatures of noise-induced temporal correlations in real-world complex signals.