Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture. Networks with higher order interactions, relevant to social groups, ecosystems and human brain, require new tools and instruments for their analysis. Gambuzza et al. propose an analytical approach which allows to find conditions for stable synchronization in many-body interaction networks.

Stability of synchronization in simplicial complexes / Gambuzza, L. V.; Di Patti, F.; Gallo, L.; Lepri, S.; Romance, M.; Criado, R.; Frasca, M.; Latora, V.; Boccaletti, S.. - In: NATURE COMMUNICATIONS. - ISSN 2041-1723. - ELETTRONICO. - 12:(2021), pp. 1255.0-1255.0. [10.1038/s41467-021-21486-9]

Stability of synchronization in simplicial complexes

Di Patti, F.;
2021

Abstract

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture. Networks with higher order interactions, relevant to social groups, ecosystems and human brain, require new tools and instruments for their analysis. Gambuzza et al. propose an analytical approach which allows to find conditions for stable synchronization in many-body interaction networks.
2021
12
0
0
Gambuzza, L. V.; Di Patti, F.; Gallo, L.; Lepri, S.; Romance, M.; Criado, R.; Frasca, M.; Latora, V.; Boccaletti, S.
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1395056
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