Turing patterns in systems with high-order interactions

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 microscropic 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.

References in corpus (6)

• The physics of higher-order interactions in complex systems
• Turing patterns in network-organized activator-inhibitor systems
• Topology-driven instabilities: the theory of pattern formation on directed networks
• Synchronization induced by directed higher-order interactions
• How limit cycles and quasi-cycles are related in systems with intrinsic noise
• Diffusion-driven instability of topological signals coupled by the Dirac operator

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• Diffusion-driven instability of topological signals coupled by the Dirac operator
• Phase chimera states on non-local hyperrings
• Emergence of geometric Turing patterns in complex networks
• Global topological synchronization of weighted simplicial complexes
• Theory of phase reduction from hypergraphs to simplicial complexes: a general route to higher-order Kuramoto models
• Pinning control of chimera states in systems with higher-order interactions
• Impact of directionality on the emergence of Turing patterns on m-directed higher-order structures
• Global Topological Dirac Synchronization
• Pattern reconstruction through generalized eigenvectors on defective networks
• A Hybrid Membership Latent Distance Model for Unsigned and Signed Integer Weighted Networks
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• On the efficiency of pairwise Hamiltonian control to desynchronize the higher-order Kuramoto model