Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917028376346624 |
|---|---|
| author | Dorchain, Marie Segnou, Wilfried Muolo, Riccardo Carletti, Timoteo |
| author_facet | Dorchain, Marie Segnou, Wilfried Muolo, Riccardo Carletti, Timoteo |
| contents | We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being 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, emerges 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04721 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures Dorchain, Marie Segnou, Wilfried Muolo, Riccardo Carletti, Timoteo Pattern Formation and Solitons Statistical Mechanics Dynamical Systems Adaptation and Self-Organizing Systems We hereby develop the theory of Turing instability for reaction-diffusion systems defined on m-directed hypergraphs, the latter being 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, emerges 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. |
| title | Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures |
| topic | Pattern Formation and Solitons Statistical Mechanics Dynamical Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2408.04721 |