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Turing patterns in systems with high-order interactions

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  • Muolo, Riccardo
  • Gallo, Luca
  • Latora, Vito
  • Frasca, Mattia
  • Carletti, Timoteo

Abstract

Turing theory of pattern formation is among the most popular theoretical means to account for the variety of spatio-temporal structures observed in Nature and, for this reason, finds applications in many different fields. While Turing patterns have been thoroughly investigated on continuous support and on networks, only a few attempts have been made towards their characterization in systems with higher-order interactions. In this paper, we propose a way to include group interactions in reaction–diffusion systems, and we study their effects on the formation of Turing patterns. To achieve this goal, we rewrite the problem originally studied by Turing in a general form that accounts for a microscopic description of interactions of any order in the form of a hypergraph, and we prove that the interplay between the different orders of interaction may either enhance or repress the emergence of Turing patterns. Our results shed light on the mechanisms of pattern-formation in systems with many-body interactions and pave the way for further extensions of Turing original framework.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922010918
    DOI: 10.1016/j.chaos.2022.112912
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    References listed on IDEAS

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    4. Malbor Asllani & Timoteo Carletti & Duccio Fanelli & Philip K. Maini, 2020. "A universal route to pattern formation in multicellular systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(7), pages 1-11, July.
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    6. Kumar, Niraj & Horsthemke, Werner, 2010. "Turing bifurcation in a reaction–diffusion system with density-dependent dispersal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(9), pages 1812-1818.
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