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• W2123269022 abstract "The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [U. Tirnakli et al., Phys. Rev. E 75, 040106(R) (2007)] to be numerically consistent with a $q$-Gaussian, the distribution which---under appropriate constraints---maximizes the nonadditive entropy ${S}_{q}$, which is the basis of nonextensive statistical mechanics. This analysis was based on a study of the tails of the distribution. We now check the entire distribution, in particular, its central part. This is important in view of a recent $q$ generalization of the central limit theorem, which states that for certain classes of strongly correlated random variables the rescaled sum approaches a $q$-Gaussian limit distribution. We numerically investigate for the logistic map with a parameter in a small vicinity of the critical point under which conditions there is convergence to a $q$-Gaussian both in the central region and in the tail region and find a scaling law involving the Feigenbaum constant $ensuremath{delta}$. Our results are consistent with a large number of already available analytical and numerical evidences that the edge of chaos is well described in terms of the entropy ${S}_{q}$ and its associated concepts." @default.
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• W2123269022 date "2009-05-11" @default.
• W2123269022 modified "2023-10-16" @default.
• W2123269022 title "Closer look at time averages of the logistic map at the edge of chaos" @default.
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• W2123269022 doi "https://doi.org/10.1103/physreve.79.056209" @default.
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