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

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

2009-03-25

arxiv.org/abs/0903.4400v2

Physica A 388 (2009) 4818

Physics

Condensed Matter

Statistical Mechanics

15 pages, 8 figures

Scientific paper

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 attractors naturally emerge, consistently with recently proved generalizations of the CLT.

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