Synchronization of oscillators with long range interaction: phase transition and anomalous finite size effects

Details Synchronization of oscillators with long range interaction: phase transition and anomalous finite size effects Synchronization of oscillators with long range interaction: phase transition and anomalous finite size effects

2002-01-18

arxiv.org/abs/cond-mat/0201337v2

Phys. Rev. E 66, 011109 (2002)

Physics

Condensed Matter

Statistical Mechanics

15 pages, 12 figures, submitted to Phys. Rev. E; Text slightly changed; References added; Fig. 9 updated

Scientific paper

10.1103/PhysRevE.66.011109

Synchronization in a lattice of a finite population of phase oscillators with algebraically decaying, non-normalized coupling is studied by numerical simulations. A critical level of decay is found, below which full locking takes place if the population contains a sufficiently large number of elements. For large number of oscillators and small coupling constant, numerical simulations and analytical arguments indicate that a phase transition separating synchronization from incoherence appears at a decay exponent value equal to the number of dimensions of the lattice. In contrast with earlier results on similar systems with normalized coupling, we have indication that for the decay exponent less than the dimensions of the lattice and for large populations, synchronization is possible even if the coupling is arbitarily weak. This finding suggests that in organisms interacting through slowly decaying signals like light or sound, collective oscillations can always be established if the population is sufficiently large.

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