Generalized Huberman-Rudnick Scaling Law And Robustness Of Q-Gaussian Probability Distributions
| Autor: | Ugur Tirnakli, Ozgur Afsar |
|---|---|
| Rok vydání: | 2013 |
| Předmět: |
Subharmonic
Scaling law Statistical Mechanics (cond-mat.stat-mech) General Physics and Astronomy FOS: Physical sciences Nonlinear Sciences - Chaotic Dynamics 01 natural sciences 010305 fluids & plasmas q-Gaussian Robustness (computer science) Iterated function 0103 physical sciences Probability distribution Statistical physics Logistic map Chaotic Dynamics (nlin.CD) 010306 general physics Scaling Condensed Matter - Statistical Mechanics Mathematics |
| Popis: | 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. Comment: 13 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|