Dynamical systems on hypergraphs

Timoteo Carletti; Duccio Fanelli

doi:10.1007/978-3-030-91374-8_5

Dynamical systems on hypergraphs

Timoteo Carletti, Duccio Fanelli

Research output: Contribution in Book/Catalog/Report/Conference proceeding › Chapter (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 language	English
Title of host publication	Higher-Order Systems
Publisher	Springer
Pages	163-180
Number of pages	18
ISBN (Electronic)	978-3-030-91374-8
ISBN (Print)	978-3-030-91376-2
DOIs	https://doi.org/10.1007/978-3-030-91374-8_5
Publication status	Published - 27 Apr 2022

Publication series

Name	Understanding Complex Systems
Publisher	Springer
ISSN (Print)	1860-0832
ISSN (Electronic)	1860-0840

Keywords

hypergraphs
Turing patterns
synchronization
Markov processes
long range interactions

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10.1007/978-3-030-91374-8_5

CarlettiFanelliv3Final published version, 499 KB

https://link.springer.com/chapter/10.1007/978-3-030-91374-8_5

Cite this

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AU - Carletti, Timoteo

AU - Fanelli, Duccio

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AB - 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.

KW - hypergraphs

KW - Turing patterns

KW - synchronization

KW - Markov processes

KW - long range interactions

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T3 - Understanding Complex Systems

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BT - Higher-Order Systems

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Dynamical systems on hypergraphs

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