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

Mathematics

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

A. Arnaudon, R. L. Peach, et al.

Discover how the generalized Sakaguchi-Kuramoto model on weighted simplicial complexes, conducted by Alexis Arnaudon and colleagues, unveils complex dynamics and partial synchronization loss in Hodge subspaces. This innovative research extends higher-order interactions in mathematical modeling, promising new insights into synchronization phenomena.

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Playback language: English
Abstract
This paper introduces a generalized Sakaguchi-Kuramoto model on weighted simplicial complexes, extending the Kuramoto model to higher-order interactions. The model incorporates linear and nonlinear frustration terms independent of simplex orientation. Simulations on increasingly complex simplicial complexes reveal complex dynamics, including partial synchronization loss in Hodge subspaces and simplicial phase re-locking under high frustration.
Publisher
Communications Physics
Published On
Aug 16, 2022
Authors
Alexis Arnaudon, Robert L. Peach, Giovanni Petri, Paul Expert
Tags
Sakaguchi-Kuramoto model
weighted simplicial complexes
higher-order interactions
synchronization
complex dynamics
frustration
Hodge subspaces

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