Dynamical systems on hypergraphs
Statistical Mechanics
2021-04-06 v1 Dynamical Systems
Pattern Formation and Solitons
Physics and Society
Abstract
We present a general framework that enables one to model high-order interaction 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.
Cite
@article{arxiv.2104.01973,
title = {Dynamical systems on hypergraphs},
author = {Timoteo Carletti and Duccio Fanelli},
journal= {arXiv preprint arXiv:2104.01973},
year = {2021}
}