Imperial College London
Alternate

DrAlexisArnaudon

Faculty of Natural Sciences, Department of Mathematics

Academic Visitor
 
 
 
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Contact

 

+44 (0)7463 328 499alexis.arnaudon Website

 
 
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Location

 

6M34Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@unpublished{Arnaudon:2022,
author = {Arnaudon, A and Peach, R and Petri, G and Expert, P},
publisher = {ArXiv},
title = {Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for  coupled oscillators on simplicial complexes},
url = {http://arxiv.org/abs/2111.11073v3},
year = {2022}
}
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RIS format (EndNote, RefMan)

TY  - UNPB
AB  - We formulate a general Kuramoto model on weighted simplicial complexes wherephases oscillators are supported on simplices of any order $k$. Crucially, weintroduce linear and non-linear frustration terms that are independent of theorientation of the $k+1$ simplices, providing a natural generalization of theSakaguchi-Kuramoto model. In turn, this provides a generalized formulation ofthe Kuramoto higher-order parameter as a potential function to write thedynamics as a gradient flow. With a selection of simplicial complexes ofincreasingly complex structure, we study the properties of the dynamics of thesimplicial Sakaguchi-Kuramoto model with oscillators on edges to highlight thecomplexity of dynamical behaviors emerging from even simple simplicialcomplexes. We place ourselves in the case where the vector of internalfrequencies of the edge oscillators lies in the kernel of the Hodge Laplacian,or vanishing linear frustration, and, using the Hodge decomposition of thesolution, we understand how the nonlinear frustration couples the dynamics inorthogonal subspaces. We discover various dynamical phenomena, such as thepartial loss of synchronization in subspaces aligned with the Hodge subspacesand the emergence of simplicial phase re-locking in regimes of highfrustration.
AU  - Arnaudon,A
AU  - Peach,R
AU  - Petri,G
AU  - Expert,P
PB  - ArXiv
PY  - 2022///
TI  - Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for  coupled oscillators on simplicial complexes
UR  - http://arxiv.org/abs/2111.11073v3
UR  - http://hdl.handle.net/10044/1/98349
ER  -
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