Stability of synchronization in simplicial complexes

Gambuzza, Lucia Valentina; Patti, Francesca Di; Gallo, Luca; Lepri, Stefano; Romance, Miguel; Criado, Roberta F. J.; Frasca, Mattia; Latora, Vito; Boccaletti, Stefano

doi:10.1038/s41467-021-21486-9

Cited by 159 publications

(117 citation statements)

References 77 publications

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“…It is also worth mentioning an alternative approach to high-order interactions which exploits the notion of simplicial complexes [16,14,41]. Largely used in the past to tackle optimisation or algebraic problems, they have been recently invoked to address problems in epidemic spreading [10,26] or synchronisation phenomena [32,22,34]. In this work we will however adopt the viewpoint of hypergraphs, to represent high-order interactions.…”

Section: Introductionmentioning

confidence: 99%

Dynamical systems on hypergraphs

2020

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We present a general framework that enables one to model high-order interaction among entangled dynamical systems, via hypergraphs. Several relevant processes can be ideally traced back to the proposed scheme. We shall here solely elaborate on the conditions that seed the spontaneous emergence of patterns, spatially heterogeneous solutions resulting from the many-body interaction between fundamental units. In particular we will focus, on two relevant settings. First, we will assume long-ranged mean field interactions between populations, and then turn to considering diffusive-like couplings. Two applications are presented, respectively to a generalised Volterra system and the Brusselator model.

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Section: Introductionmentioning

confidence: 99%

Dynamical systems on hypergraphs

2020

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“…Given the space limitation, we will not be able to treat here all the different approaches proposed to characterize the synchronization transitions in higherorder networks, such as those based on the master stability function [120,121] and cluster synchronization [122,123].…”

Section: Simplicial Synchronizationmentioning

confidence: 99%

Higher-Order Networks

Bianconi

2021

111

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Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

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“…Different from the simplicial complex approach, the hypergraph approach does not require the existence of all lower-order interactions. A range of dynamical processes such as social contagion [14,26], oscillator synchronization [27,28], random walks [29,30], opinion dynamics [31,32] and naming games [33] have been studied on these higher-order system models in the last few years.…”

Section: Introductionmentioning

confidence: 99%

A system model of three-body interactions in complex networks: consensus and conservation

Shang

2022

Proc. R. Soc. A.

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Networked complex systems in a wide range of physics, biology and social sciences involve synergy among multiple agents beyond pairwise interactions. Higher-order mathematical structures such as hypergraphs have been increasingly popular in modelling and analysis of complex dynamical behaviours. Here, we study a simple three-body consensus model, which favourably incorporates higher-order network interactions, higher-order dimensional states, the group reinforcement effect and the social homophily principle. The model features asymmetric roles of acting agents using modulating functions. We analytically establish sufficient conditions for nonlinear consensus and conservation of states for agents with both discrete-time and continuous-time dynamics. We show that higher-order interactions encoded in three-body edges give rise to consensus and conservation for systems with gravity-like and Heaviside-like modulating functions. Furthermore, we illustrate our theoretical results with numerical simulations and examine the system convergence time through a network depreciation process.

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Stability of synchronization in simplicial complexes

Cited by 159 publications

References 77 publications

Dynamical systems on hypergraphs

Dynamical systems on hypergraphs

Higher-Order Networks

A system model of three-body interactions in complex networks: consensus and conservation

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