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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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    1. Jacopo Grilli & György Barabás & Matthew J. Michalska-Smith & Stefano Allesina, 2017. "Higher-order interactions stabilize dynamics in competitive network models," Nature, Nature, vol. 548(7666), pages 210-213, August.
    2. Iacopo Iacopini & Giovanni Petri & Alain Barrat & Vito Latora, 2019. "Simplicial models of social contagion," Nature Communications, Nature, vol. 10(1), pages 1-9, December.
    3. Krawiecki, A., 2014. "Chaotic synchronization on complex hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 65(C), pages 44-50.
    4. Shi, Tian & Qin, Yi & Yang, Qi & Ma, Zhongjun & Li, Kezan, 2023. "Synchronization of directed uniform hypergraphs via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 615(C).
    5. Muolo, Riccardo & Gallo, Luca & Latora, Vito & Frasca, Mattia & Carletti, Timoteo, 2023. "Turing patterns in systems with high-order interactions," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    6. L. V. Gambuzza & F. Patti & L. Gallo & S. Lepri & M. Romance & R. Criado & M. Frasca & V. Latora & S. Boccaletti, 2021. "Stability of synchronization in simplicial complexes," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    7. Li, Kezan & Lin, Yingmei & Wang, Junyi, 2024. "Synchronization of multi-directed hypergraphs via adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    8. Carletti, Timoteo & Fanelli, Duccio, 2022. "Theory of synchronisation and pattern formation on time varying networks," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    9. Malbor Asllani & Joseph D. Challenger & Francesco Saverio Pavone & Leonardo Sacconi & Duccio Fanelli, 2014. "The theory of pattern formation on directed networks," Nature Communications, Nature, vol. 5(1), pages 1-9, December.
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