Dynamical systems on hypergraphs

Timoteo Carletti, Duccio Fanelli, Sara Nicoletti

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Abstract

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.
Original languageEnglish
Number of pages16
JournalJournal of Physics: Complexity
Volume1
Issue number3
DOIs
Publication statusPublished - 17 Aug 2020

Keywords

  • hypergraphs
  • dynamical systems
  • Turing patterns
  • Synchronisation
  • Master Stability Function
  • nonlinear oscillators

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