Generalising the Kuramoto model for the study of neuronal synchronisation in the brain
type: Item
instance of: scholarly article
title: Generalising the Kuramoto model for the study of neuronal synchronisation in the brain
zbMATH Open document ID: 1120.34024
author: D. Cumin
author: C. P. Unsworth
published in: Physica D
publication date: 2007-03-08T00:00:00Z
review text: The paper presents a numerical analysis of the coupled system \[ \dot \theta_i = \omega_i(t) + \frac{1}{N} \sum_{j=1}^N K_{i,j}(t) \sin (\theta_j-\theta_i), \quad i=1,\dots,4, \] which is a generalization of the Kuramoto system to the case of time-dependent frequencies \(\omega_i(t)\), and coupling \(K_{i,j}(t)\). The authors study the behavior of the order parameter \(re^{i\psi}=(1/N)\sum_{j=1}^N e^i\theta_j\) for different cases of \(K_{i,j}(t)\), corresponding to different connection architectures, such as linear array, ring, or all-to-all.
reviewed by: S. Yanchuk
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34D05
Mathematics Subject Classification ID: 37N25
zbMATH DE Number: 5131658
zbMATH Keywords: coupled oscillators
zbMATH Keywords: synchronization
zbMATH Keywords: brain
zbMATH Keywords: neuron
Wikidata QID: Q29028650
MaRDI profile type: Publication
full work available at URL: j.physd.2006.12.004
OpenAlex ID: W2065407206
cites work: Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients
cites work: From Kuramoto to Crawford: Exploring the onset of synchronization in population of coupled oscillators
cites work: Chemical oscillations, waves, and turbulence
cites work: A shocking display of synchrony
cites work: Q3654677
DOI: 10.1016/J.PHYSD.2006.12.004
description: scientific article; zbMATH DE number 5131658