Metastable state en route to traveling-wave synchronization state

TL;DR

This paper investigates a metastable state in the Kuramoto model with mixed couplings, revealing a hybrid phase transition characterized by long-lasting fluctuations and controllable synchronization dynamics, with potential implications for understanding consciousness recovery.

Contribution

It introduces a detailed explanation of metastability in the Kuramoto model with mixed signs, highlighting the role of phase space flow and saddle points in long-lasting critical behavior.

Findings

Metastable state exhibits large fluctuations before synchronization.

Long-lasting critical behavior is linked to phase space flow within bounded regions.

The duration of metastability can be controlled by adjusting inhibitory/excitatory interactions.

Abstract

The Kuramoto model with mixed signs of couplings is known to produce a traveling-wave synchronized state. Here, we consider an abrupt synchronization transition from the incoherent state to the traveling-wave state through a long-lasting metastable state with large fluctuations. Our explanation of the metastability is that the dynamic flow remains within a limited region of phase space and circulates through a few active states bounded by saddle and stable fixed points. This complex flow generates a long-lasting critical behavior, a signature of a hybrid phase transition. We show that the long-lasting period can be controlled by varying the density of inhibitory/excitatory interactions. We discuss a potential application of this transition behavior to the recovery process of human consciousness.