Generalized Huberman-Rudnick scaling law and robustness of q-Gaussian probability distributions

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Afsar O. , Tirnakli U.

EPL, cilt.101, 2013 (SCI İndekslerine Giren Dergi) identifier identifier


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. Copyright (C) EPLA, 2013