Abstract

The entrainment transition of coupled random frequency oscillators presents a long-standingproblem in nonlinear physics. The onset of entrainment in populations of large but finitesize exhibits strong sensitivity to fluctuations in the oscillator density at the synchronizingfrequency. This is the source for the unusual values assumed by the correlation size exponentν′. Locally coupledoscillators on a d-dimensional lattice exhibit two types of frequency entrainment in the thermodynamic limit: symmetry-breakingat d > 4 and aggregation of compact synchronized domains in three and four dimensions. Variouscritical properties of the transition are well captured by finite-size scaling relations withsimple yet unconventional exponent values.

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