Metastable state en route to traveling-wave synchronization state
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.
Cite
@article{arxiv.1802.07409,
title = {Metastable state en route to traveling-wave synchronization state},
author = {Jinha Park and B. Kahng},
journal= {arXiv preprint arXiv:1802.07409},
year = {2018}
}