Eur. Phys. J. B 67, 577-584 (2009)
https://doi.org/10.1140/epjb/e2009-00054-2

Nonextensivity at the edge of chaos of a new universality class of one-dimensional unimodal dissipative maps

¹ Universidad Politécnica de Madrid, Pza. Cardenal Cisneros N. 4, 28040 Madrid, Spain
² Centro Brasileiro de Pesquisas Fisicas and National Institute of Science and Technology for Complex Systems Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil
³ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM, 87501, USA

Corresponding author: ^a guiomar.ruiz@upm.es

Received: 21 November 2008
Revised: 26 January 2009
Published online: 18 February 2009

Abstract

We introduce a new universality class of one-dimensional unimodal dissipative maps. The new family, from now on referred to as the (z₁, z₂)-logarithmic map, corresponds to a generalization of the z-logistic map. The Feigenbaum-like constants of these maps are determined. It has been recently shown that the probability density of sums of iterates at the edge of chaos of the z-logistic map is numerically consistent with a q-Gaussian, the distribution which, under appropriate constraints, optimizes the nonadditive entropy S_q. We focus here on the presently generalized maps to check whether they constitute a new universality class with regard to q-Gaussian attractor distributions. We also study the generalized q-entropy production per unit time on the new unimodal dissipative maps, both for strong and weak chaotic cases. The q-sensitivity indices are obtained as well. Our results are, like those for the z-logistic maps, numerically compatible with the q-generalization of a Pesin-like identity for ensemble averages.