Journal
CHAOS SOLITONS & FRACTALS
Volume 166, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.chaos.2022.112912
Keywords
Pattern formation; High-order interactions; Turing instability; Nonlinear diffusion; Hypergraphs; Simplicial complexes
Ask authors/readers for more resources
Turing theory is widely used to explain the spatio-temporal structures observed in Nature. This paper proposes a method to include group interactions in reaction-diffusion systems and examines their effects on Turing pattern formation. Results demonstrate the mechanisms of pattern formation in systems with many-body interactions and provide a basis for further extensions of the Turing framework.
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 reactiondiffusion 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.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available