Noisy coupled logistic maps in the vicinity of chaos threshold

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 ϵ and the noise width σmax, was recently introduced by Pluchino et al. [Phys. Rev. E 87, 022910 (2013)]. They detected, for the time averaged returns with characteristic return time τ, possible connections with q-Gaussians, the distributions which optimise, under appropriate constraints, the nonadditive entropy, Sq, 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,τ,ϵ,σmax). 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.