Closer look at time averages of the logistic map at the edge of chaos
Küçük Resim Yok
Tarih
2009
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Amer Physical Soc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
The probability distribution of sums of iterates of the logistic map at the edge of chaos has been recently shown [U. Tirnakli , 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 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.
Açıklama
Anahtar Kelimeler
chaos, critical points, entropy, probability, random processes
Kaynak
Physical Review E
WoS Q Değeri
Q1
Scopus Q Değeri
N/A
Cilt
79
Sayı
5
