Entrainment transition in populations of random frequency oscillators

Abstract

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.

published version

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