Turing patterns in systems with high-order interactions

Riccardo Muolo, Luca GALLO, Vito Latora, Mattia Frasca, Timoteo Carletti

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Article number112912
Number of pages10
Journal Chaos, Solitons & Fractals: the interdisciplinary journal of nonlinear science, and nonequilibrium and complex phenomena
Issue number112912
Early online dateNov 2022
Publication statusPublished - 1 Jan 2023


  • Pattern formation
  • High-order interactions
  • Turing instability
  • Nonlinear diffusion
  • Hypergraphs
  • Simplicial complexes


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