# Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexes

@inproceedings{Arnaudon2021ConnectingHA, title={Connecting Hodge and Sakaguchi-Kuramoto: a mathematical framework for coupled oscillators on simplicial complexes}, author={Alexis Arnaudon and Robert L. Peach and Giovanni Petri and Paul Expert}, year={2021} }

We formulate a general Kuramoto model on weighted simplicial complexes where phases oscillators are supported on simplices of any order k . Crucially, we introduce linear and non-linear frustration terms that are independent of the orientation of the k +1 simplices, providing a natural generalization of the Sakaguchi-Kuramoto model. In turn, this provides a generalized formulation of the Kuramoto higher-order parameter as a potential function to write the dynamics as a gradient ﬂow. With a…

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