Arnaudon, Alexis;
Peach, Robert L;
Petri, Giovanni;
Expert, Paul;
(2022)
Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes.
Communications Physics
, 5
(1)
, Article 211. 10.1038/s42005-022-00963-7.
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Abstract
Phase synchronizations in models of coupled oscillators such as the Kuramoto model have been widely studied with pairwise couplings on arbitrary topologies, showing many unexpected dynamical behaviors. Here, based on a recent formulation the Kuramoto model on weighted simplicial complexes with phases supported on simplices of any order k, we introduce linear and non-linear frustration terms independent of the orientation of the k + 1 simplices, as a natural generalization of the Sakaguchi-Kuramoto model to simplicial complexes. With increasingly complex simplicial complexes, we study the the dynamics of the edge simplicial Sakaguchi-Kuramoto model with nonlinear frustration to highlight the complexity of emerging dynamical behaviors. We discover various dynamical phenomena, such as the partial loss of synchronization in subspaces aligned with the Hodge subspaces and the emergence of simplicial phase re-locking in regimes of high frustration.
| Type: | Article |
|---|---|
| Title: | Connecting Hodge and Sakaguchi-Kuramoto through a mathematical framework for coupled oscillators on simplicial complexes |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1038/s42005-022-00963-7 |
| Publisher version: | https://doi.org/10.1038/s42005-022-00963-7 |
| Language: | English |
| Additional information: | © 2022 Springer Nature Limited. This article is licensed under a Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/). |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > School of Life and Medical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10154875 |
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