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28 March 2024
 
  » arxiv » nlin.CD/0002018

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Chaos or Noise - Difficulties of a Distinction
M. Cencini ; M. Falcioni ; H. Kantz ; E. Olbrich ; A. Vulpiani ;
Date 14 Feb 2000
Journal Phys. Rev. E 62, 427-437 (2000)
Subject Chaotic Dynamics; Statistical Mechanics; Data Analysis, Statistics and Probability | nlin.CD cond-mat.stat-mech physics.data-an
AbstractIn experiments, the dynamical behavior of systems is reflected in time series. Due to the finiteness of the observational data set it is not possible to reconstruct the invariant measure up to arbitrary fine resolution and arbitrary high embedding dimension. These restrictions limit our ability to distinguish between signals generated by different systems, such as regular, chaotic or stochastic ones, when analyzed from a time series point of view. We propose to classify the signal behavior, without referring to any specific model, as stochastic or deterministic on a certain scale of the resolution $epsilon$, according to the dependence of the $(epsilon, au)$-entropy, $h(epsilon, au)$, and of the finite size Lyapunov exponent, $lambda(epsilon)$, on $epsilon$.
Source arXiv, nlin.CD/0002018
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