Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures

Marie Dorchain, Wilfried Segnou, Riccardo Muolo and Timoteo Carletti

Chaos, Solitons & Fractals, 2024, vol. 189, issue P2

Abstract: We hereby develop the theory of Turing instability for reaction–diffusion systems defined on m-directed hypergraphs, the latter being a generalization of hypergraphs where nodes forming hyperedges can be shared into two disjoint sets, the head nodes and the tail nodes. This framework encodes thus for a privileged direction for the reaction to occur: the joint action of tail nodes is a driver for the reaction involving head nodes. It thus results a natural generalization of directed networks. Based on a linear stability analysis, we have shown the existence of two Laplace matrices, allowing to analytically prove that Turing patterns, stationary or wave-like, emerge for a much broader set of parameters in the m-directed setting. In particular, directionality promotes Turing instability, otherwise absent in the symmetric case. Analytical results are compared to simulations performed by using the Brusselator model defined on a m-directed d-hyperring, as well as on a m-directed random hypergraph.

Keywords: Turing patterns; Higher-order structures; m-directed hypergraphs; Hypergraphs; Brusselator model (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077924012827
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012827

DOI: 10.1016/j.chaos.2024.115730

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().