Dynamical systems on hypergraphs

Timoteo Carletti, Duccio Fanelli, Sara Nicoletti

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Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider a general class of dynamical systems anchored on hypergraphs. Hyperedges of arbitrary size ideally encircle individual units so as to account for multiple, simultaneous interactions. These latter are mediated by a combinatorial Laplacian, that is here introduced and characterised. The formalism of the master stability function is adapted to the present setting. Turing patterns and the synchronisation of non linear (regular and chaotic) oscillators are studied, for a general class of systems evolving on hypergraphs. The response to externally imposed perturbations bears the imprint of the higher order nature of the interactions.
langue originaleAnglais
Nombre de pages16
journalJournal of Physics: Complexity
Numéro de publication3
Les DOIs
Etat de la publicationPublié - 17 août 2020

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