Entrainment transition in populations of random frequency oscillators

Details Entrainment transition in populations of random frequency oscillators Entrainment transition in populations of random frequency oscillators

2007-01-26

arxiv.org/abs/cond-mat/0701646v2

Phys. Rev. Lett. 99, 184101 (2007)

Physics

Condensed Matter

Statistical Mechanics

published version

Scientific paper

10.1103/PhysRevLett.99.184101

The entrainment transition of coupled random frequency oscillators is revisited. The Kuramoto model (global coupling) is shown to exhibit unusual sample-dependent finite size effects leading to a correlation size exponent $\bar\nu=5/2$. Simulations of locally coupled oscillators in $d$-dimensions reveal two types of frequency entrainment: mean-field behavior at $d>4$, and aggregation of compact synchronized domains in three and four dimensions. In the latter case, scaling arguments yield a correlation length exponent $\nu=2/(d-2)$, in good agreement with numerical results.

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