Collective phase synchronization in locally-coupled limit-cycle oscillators

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

2003-12-23

arxiv.org/abs/cond-mat/0312599v1

Phys. Rev. E 70, 045204 (2004)

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1103/PhysRevE.70.045204

We study collective behavior of locally-coupled limit-cycle oscillators with scattered intrinsic frequencies on $d$-dimensional lattices. A linear analysis shows that the system should be always desynchronized up to $d=4$. On the other hand, numerical investigation for $d= 5$ and 6 reveals the emergence of the synchronized (ordered) phase via a continuous transition from the fully random desynchronized phase. This demonstrates that the lower critical dimension for the phase synchronization in this system is $d_{l}=4$

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