Multiorder Laplacian for Kuramoto Dynamics with Higher-Order Interactions

Maxime Lucas*, Giulia Cencetti, Federico Battiston

*Corresponding author for this work

Research output: Contribution to Book/Report typesChapterpeer-review

Abstract (may include machine translation)

Many real-world systems are characterised by higher-order interactions, where influences among units involve more than two nodes at a time, and which can significantly affect the emergence of collective behaviors. A paradigmatic case is that of synchronization, occuring when oscillators reach coherent dynamics through their mutual couplings, and which is known to display richer collective phenomena when connections are not limited to simple dyads. Here, we consider an extension of the Kuramoto model with higher-order interactions, where oscillators can interact in groups of any size, arranged in any arbitrary complex topology. We present a new operator, the multiorder Laplacian, which allows us to treat the system analytically and that can be used to assess the stability of synchronization in general higher-order networks. Our spectral approach, originally devised for Kuramoto dynamics, can be extended to a wider class of dynamical processes beyond pairwise interactions, advancing our quantitative understanding of how higher-order interactions impact network dynamics.

Original languageEnglish
Title of host publicationUnderstanding Complex Systems
PublisherSpringer Science and Business Media Deutschland GmbH
Pages233-247
Number of pages15
DOIs
StatePublished - 2022

Publication series

NameUnderstanding Complex Systems
ISSN (Print)1860-0832
ISSN (Electronic)1860-0840

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