Noisy coupled logistic maps in the vicinity of chaos threshold


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Tirnakli U. , TSALLIS C.

CHAOS, vol.26, no.4, 2016 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 26 Issue: 4
  • Publication Date: 2016
  • Doi Number: 10.1063/1.4947548
  • Title of Journal : CHAOS

Abstract

We focus on a linear chain of N first-neighbor-coupled logistic maps in the vicinity of their edge of chaos in the presence of a common noise. This model, characterised by the coupling strength epsilon and the noise width sigma(max), was recently introduced by Pluchino et al. [Phys. Rev. E 87, 022910 ( 2013)]. They detected, for the time averaged returns with characteristic return time tau, possible connections with q-Gaussians, the distributions which optimise, under appropriate constraints, the nonadditive entropy, S-q, basis of nonextensive statistics mechanics. Here, we take a closer look on this model, and numerically obtain probability distributions which exhibit a slight asymmetry for some parameter values, in variance with simple q-Gaussians. Nevertheless, along many decades, the fitting with q-Gaussians turns out to be numerically very satisfactory for wide regions of the parameter values, and we illustrate how the index q evolves with (N, tau, epsilon, sigma(max)). It is nevertheless instructive on how careful one must be in such numerical analysis. The overall work shows that physical and/or biological systems that are correctly mimicked by this model are thermostatistically related to nonextensive statistical mechanics when time-averaged relevant quantities are studied. Published by AIP Publishing.