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

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  • Dorchain, Marie
  • Segnou, Wilfried
  • Muolo, Riccardo
  • Carletti, Timoteo

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.

Suggested Citation

  • Dorchain, Marie & Segnou, Wilfried & Muolo, Riccardo & Carletti, Timoteo, 2024. "Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p2:s0960077924012827
    DOI: 10.1016/j.chaos.2024.115730
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