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Entrainment transition in populations of random frequency oscillators

Hyunsuk Hong·Hugues Chate·Hyunggyu Park·Lei-Han Tang
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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 $\barν=5/2$. 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 $ν=2/(d-2)$, in good agreement with numerical results.

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Hyunsuk Hong, Hugues Chate, Hyunggyu Park, Lei-Han Tang. 2007-11-14. Entrainment transition in populations of random frequency oscillators. https://doi.org/10.1103/physrevlett.99.184101

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