Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-11-25
Nonlinear Sciences
Chaotic Dynamics
9 pages, 1 figure, to appear in a special issue of JSTAT dedicated to Statphys24
Scientific paper
The entrainment transition of coupled random frequency oscillators presents a long-standing problem in nonlinear physics. The onset of entrainment in populations of large but finite size exhibits strong sensitivity to fluctuations in the oscillator density at the synchronizing frequency. This is the source for the unusual values assumed by the correlation size exponent $\nu'$. Locally coupled oscillators on a $d$-dimensional lattice exhibit two types of frequency entrainment: symmetry-breaking at $d > 4$, and aggregation of compact synchronized domains in three and four dimensions. Various critical properties of the transition are well captured by finite-size scaling relations with simple yet unconventional exponent values.
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