Connecting hodge and sakaguchi-kuramoto through a mathematical framework for coupled oscillators on simplicial complexes

Arnaudon, Alexis, Peach, Robert L, Petri, Giovanni and Expert, Paul (2022) Connecting hodge and sakaguchi-kuramoto through a mathematical framework for coupled oscillators on simplicial complexes. Communications Physics, 5 (1). p. 211.

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.

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Official URL:	https://doi.org/10.1038/s42005-022-00963-7
Item Type:	Article
Disciplines:	Network Science
Depositing User:	Giovanni Petri
Date Deposited:	09 Oct 2023 09:23
Last Modified:	29 Oct 2024 13:32
URI:	https://nul.repository.guildhe.ac.uk/id/eprint/1026

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