A unified framework for simplicial Kuramoto models.

Autor:	Nurisso M; CENTAI Institute, Turin 10138, Italy.; Dipartimento di Scienze Matematiche, Politecnico di Torino, Turin 10129, Italy.; SmartData@PoliTO Center, Politecnico di Torino, Turin 10129, Italy., Arnaudon A; Blue Brain Project, École polytechnique fédérale de Lausanne (EPFL), Campus Biotech, 1202 Geneva, Switzerland., Lucas M; CENTAI Institute, Turin 10138, Italy., Peach RL; Department of Neurology, University Hospital Würzburg, Würzburg 97080, Germany.; Department of Brain Sciences, Imperial College London, London SW7 2AZ, United Kingdom., Expert P; UCL Global Business School for Health, UCL, London WC1E 6BT, United Kingdom., Vaccarino F; Dipartimento di Scienze Matematiche, Politecnico di Torino, Turin 10129, Italy.; SmartData@PoliTO Center, Politecnico di Torino, Turin 10129, Italy., Petri G; CENTAI Institute, Turin 10138, Italy.; MT Scuola Alti Studi Lucca, Lucca 55100, Italy.; NPLab, Network Science Institute, Northeastern University London, London E1W 1LP, United Kingdom.
Jazyk:	angličtina
Zdroj:	Chaos (Woodbury, N.Y.) [Chaos] 2024 May 01; Vol. 34 (5).
DOI:	10.1063/5.0169388
Abstrakt:	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. (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)
Databáze:	MEDLINE
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