Collective synchronization in spatially extended systems of coupled oscillators with random frequencies

Details Collective synchronization in spatially extended systems of coupled oscillators with random frequencies Collective synchronization in spatially extended systems of coupled oscillators with random frequencies

2004-08-26

arxiv.org/abs/cond-mat/0408553v1

Physics

Condensed Matter

Statistical Mechanics

18 pages, 18 figures

Scientific paper

10.1103/PhysRevE.72.036217

We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over $d$-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored analytically in the linear (strong-coupling) regime and numerically in the nonlinear (weak-coupling) regime. Our analysis shows that the oscillator phases are always desynchronized up to $d=4$, which implies the lower critical dimension $d_{l}^{P}=4$ for phase synchronization. On the other hand, the oscillators behave collectively in frequency (phase velocity) even in three dimensions ($d=3$), indicating that the lower critical dimension for frequency entrainment is $d_{l}^{F}=2$. Nonlinear effects due to periodic nature of limit-cycle oscillators are found to become significant in the weak-coupling regime: So-called {\em runaway oscillators} destroy the synchronized (ordered) phase and there emerges a fully random (disordered) phase. Critical behavior near the synchronization transition into the fully random phase is unveiled via numerical investigation. Collective behavior of globally-coupled oscillators is also examined and compared with that of locally coupled oscillators.

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