Dynamical systems on hypergraphs

Timoteo Carletti, Duccio Fanelli

Research output: Contribution in Book/Catalog/Report/Conference proceedingChapter (peer-reviewed)peer-review

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Abstract

We present a general framework that enables one to model high-order interactions among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate on the conditions that seed the spontaneous emergence of patterns, spatially heterogeneous solutions resulting from the many-body interaction between fundamental units. In particular we will focus, on two relevant settings. First, we will assume long-ranged mean field interactions between populations, and then turn to considering diffusive-like couplings. Two applications are presented, respectively to a generalised Volterra system and the Brusselator model.
Original languageEnglish
Title of host publicationHigher-Order Systems
PublisherSpringer
Pages163-180
Number of pages18
ISBN (Electronic)978-3-030-91374-8
ISBN (Print)978-3-030-91376-2
DOIs
Publication statusPublished - 27 Apr 2022

Publication series

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

Keywords

  • hypergraphs
  • Turing patterns
  • synchronization
  • Markov processes
  • long range interactions

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