Collective phase synchronization in locally-coupled limit-cycle oscillators

TL;DR

This paper investigates how locally-coupled oscillators with diverse intrinsic frequencies synchronize across different dimensions, revealing a critical dimension at which collective synchronization emerges.

Contribution

It identifies the lower critical dimension for phase synchronization in such systems as four, combining linear analysis and numerical simulations.

Findings

Desynchronization persists up to four dimensions.

Synchronization occurs in five and six dimensions via a continuous transition.

Lower critical dimension for synchronization is determined to be four.

Abstract

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 $d_{l}=4$