Generalized Huberman-Rudnick scaling law and robustness of q-Gaussian probability distributions
Articles > Article · 2013
Authors: Özgür AFŞAR, Uğur TIRNAKLI
EPL (Europhysics Letters), Journal Indexed in SCI Expanded, International, WoS, 2013, vol 101, pp 20003-20003
DOI: 10.1209/0295-5075/101/20003
Summary
We generalize Huberman-Rudnick universal scaling law for all periodic windows of the logistic map and show the robustness of $q$-Gaussian probability distributions in the vicinity of chaos threshold. Our scaling relation is universal for the self-similar windows of the map which exhibit period-doubling subharmonic bifurcations. Using this generalized scaling argument, for all periodic windows, as chaos threshold is approached, a developing convergence to $q$-Gaussian is numerically obtained both in the central regions and tails of the probability distributions of sums of iterates.