Central limit behavior in the Kuramoto model at the “edge of chaos”

Giovanna Miritello, Alessandro Pluchino and Andrea Rapisarda

Physica A: Statistical Mechanics and its Applications, 2009, vol. 388, issue 23, 4818-4826

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.

Keywords: Kuramoto model; Phase transitions; Central Limit Theorem; Nonextensive thermostatistics (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:388:y:2009:i:23:p:4818-4826

DOI: 10.1016/j.physa.2009.08.023

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