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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.
The stationary distributions of sums of positions of trajectories generated by the logistic map have been found to follow a basic renormalization group (RG) structure: a nontrivial fixed-point multi-scale distribution at the period-doubling onset of
In this paper, the scaling-law vector calculus, which is related to the connection between the vector calculus and the scaling law in fractal geometry, is addressed based on the Leibniz derivative and Stieltjes integral for the first time. The Gauss-
We study the collision frequencies of particles in the weakly and highly ionized plasmas with the power-law q-distributions in nonextensive statistics. We derive the average collision frequencies of neutral-neutral particle, electron-neutral particle
Weight at delivery is a standard cumulative measure of placental growth. But weight is a crude summary of other placental characteristics, such as the size and shape of the chorionic plate and the location of the umbilical cord insertion. Distributio
The Nearest Neighbour Spacing (NNS) distribution can be computed for generalized symmetric 2x2 matrices having different variances in the diagonal and in the off-diagonal elements. Tuning the relative value of the variances we show that the distribut