Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions

Abstract

When describing complex interconnected systems, one often has to go beyond the standard network description to account for generalized interactions. Here, we establish a unified framework to simplify the stability analysis of cluster synchronization patterns for a wide range of generalized networks, including hypergraphs, multilayer networks, and temporal networks. The framework is based on finding a simultaneous block diagonalization of the matrices encoding the synchronization pattern and the network topology. As an application, we use simultaneous block diagonalization to unveil an intriguing type of chimera states that appear only in the presence of higher-order interactions. The unified framework established here can be extended to other dynamical processes and can facilitate the discovery of emergent phenomena in complex systems with generalized interactions.

Published version. Part of the Focus Collection on higher-order interaction networks. The code for the simultaneous block diagonalization algorithm is available at https://github.com/y-z-zhang/SBD

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Cited by in corpus (24)

• The physics of higher-order interactions in complex systems
• Dynamics on higher-order networks: A review
• Higher-order interactions shape collective dynamics differently in hypergraphs and simplicial complexes
• The synchronized dynamics of time-varying networks
• Higher-order simplicial synchronization of coupled topological signals
• Higher-order interactions promote chimera states
• The dynamic nature of percolation on networks with triadic interactions
• Synchronization in temporal simplicial complexes
• Deeper but smaller: Higher-order interactions increase linear stability but shrink basins
• Multilayer Network Science: from Cells to Societies
• Hypergraph reconstruction from dynamics
• Turing patterns on discrete topologies: from networks to higher-order structures
• Network Alignment
• Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators
• Collective dynamics on higher-order networks
• Global topological synchronization of weighted simplicial complexes
• Triadic percolation induces dynamical topological patterns in higher-order networks
• On the Reachability and Controllability of Temporal Continuous-Time Linear Networks: A Generic Analysis
• Hyper-diffusion on multiplex networks
• Measuring dynamical systems on directed hyper-graphs
• Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks
• Bound entangled states are useful in prepare-and-measure scenarios
• Inference of time-ordered multibody interactions
• Controlling Complex Systems