We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.

Central Limit Behavior in the Kuramoto model at the 'Edge of Chaos'

PLUCHINO, ALESSANDRO;RAPISARDA, Andrea
2009-01-01

Abstract

We study the relationship between chaotic behavior and the Central Limit Theorem (CLT) in the Kuramoto model. We calculate sums of angles at equidistant times along deterministic trajectories of single oscillators and we show that, when chaos is sufficiently strong, the Pdfs of the sums tend to a Gaussian, consistently with the standard CLT. On the other hand, when the system is at the “edge of chaos” (i.e. in a regime with vanishing Lyapunov exponents), robust q-Gaussian-like limit distributions naturally emerge, consistently with recently proved generalizations of the CLT.
2009
Central limit theorem; edge of chaos; generalized statistical mechanics
File in questo prodotto:
File Dimensione Formato  
MIRITELLO PLUCHINO RAPISARDA PHYSICA A 388(2009)4818.pdf

solo gestori archivio

Tipologia: Versione Editoriale (PDF)
Licenza: NON PUBBLICO - Accesso privato/ristretto
Dimensione 2.48 MB
Formato Adobe PDF
2.48 MB Adobe PDF   Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/4127
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 28
  • ???jsp.display-item.citation.isi??? 26
social impact