Dynamical systems on hypergraphs

被引:72
作者
Carletti, Timoteo [1 ]
Fanelli, Duccio [2 ,3 ]
Nicoletti, Sara [2 ,3 ,4 ]
机构
[1] Univ Namur, Namur Inst Complex Syst, NaXys, Rempart Vierge 8, B-5000 Namur, Belgium
[2] Univ Firenze, CSDC, Dipartimento Fis & Astron, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy
[3] Ist Nazl Fis Nucl, Via G Sansone 1, I-50019 Sesto Fiorentino, Italy
[4] Univ Firenze, Dipartimento Ingn Informaz, Via S Marta 3, I-50139 Florence, Italy
来源
JOURNAL OF PHYSICS-COMPLEXITY | 2020年 / 1卷 / 03期
关键词
hypergraphs; master stability function; synchronisation; Turing patterns; dynamical systems; SYMMETRY-BREAKING INSTABILITIES; GLOBAL DYNAMICS; PATTERN-FORMATION; SPACE DEBRIS; COMPLEX; SYNCHRONIZATION; DIFFUSION; RESONANCE; STABILITY; NETWORKS;
D O I
10.1088/2632-072X/aba8e1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider a general class of dynamical systems anchored on hypergraphs. Hyperedges of arbitrary size ideally encircle individual units so as to account for multiple, simultaneous interactions. These latter are mediated by a combinatorial Laplacian, that is here introduced and characterised. The formalism of the master stability function is adapted to the present setting. Turing patterns and the synchronisation of non linear (regular and chaotic) oscillators are studied, for a general class of systems evolving on hypergraphs. The response to externally imposed perturbations bears the imprint of the higher order nature of the interactions.
引用
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页数:16
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