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

Abstract

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.

18 pages, 18 figures

References in corpus (1)

• Collective phase synchronization in locally-coupled limit-cycle oscillators

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