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A unified framework for simplicial Kuramoto models

Nurisso, Marco; Arnaudon, Alexis; Lucas, Maxime; Peach, Robert L; Expert, Paul; Vaccarino, Francesco; Petri, Giovanni; (2024) A unified framework for simplicial Kuramoto models. Chaos: An Interdisciplinary Journal of Nonlinear Science , 34 (5) , Article 053118. 10.1063/5.0169388. Green open access

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Abstract

Simplicial Kuramoto models have emerged as a diverse and intriguing class of models describing oscillators on simplices rather than nodes. In this paper, we present a unified framework to describe different variants of these models, categorized into three main groups: “simple” models, “Hodge-coupled” models, and “order-coupled” (Dirac) models. Our framework is based on topology and discrete differential geometry, as well as gradient systems and frustrations, and permits a systematic analysis of their properties. We establish an equivalence between the simple simplicial Kuramoto model and the standard Kuramoto model on pairwise networks under the condition of manifoldness of the simplicial complex. Then, starting from simple models, we describe the notion of simplicial synchronization and derive bounds on the coupling strength necessary or sufficient for achieving it. For some variants, we generalize these results and provide new ones, such as the controllability of equilibrium solutions. Finally, we explore a potential application in the reconstruction of brain functional connectivity from structural connectomes and find that simple edge-based Kuramoto models perform competitively or even outperform complex extensions of node-based models.

Type: Article
Title: A unified framework for simplicial Kuramoto models
Location: United States
Open access status: An open access version is available from UCL Discovery
DOI: 10.1063/5.0169388
Publisher version: http://dx.doi.org/10.1063/5.0169388
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences
URI: https://discovery-pp.ucl.ac.uk/id/eprint/10199423
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