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When describing complex interconnected systems, one often has to go beyondthe standard network description to account for generalized interactions. Here,we establish a unified framework to simplify the stability analysis of clustersynchronization patterns for a wide range of generalized networks, includinghypergraphs, multilayer networks, and temporal networks. The framework is basedon finding a simultaneous block diagonalization of the matrices encoding thesynchronization pattern and the network topology. As an application, we usesimultaneous block diagonalization to unveil an intriguing type of chimerastates that appear only in the presence of higher-order interactions. Theunified framework established here can be extended to other dynamical processesand can facilitate the discovery of emergent phenomena in complex systems withgeneralized interactions.

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