Symmetry-independent stability analysis of synchronization patterns

Abstract

The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks. However, to make further progress we must overcome the limitations of this celebrated formalism, which focuses on global synchronization and requires both the oscillators and their interaction functions to be identical, while many systems of interest are inherently heterogeneous and exhibit complex synchronization patterns. Here, we establish a generalization of the MSF formalism that can characterize the stability of any cluster synchronization pattern, even when the oscillators and/or their interaction functions are nonidentical. The new framework is based on finding the finest simultaneous block diagonalization of matrices in the variational equation and does not rely on information about network symmetry. This leads to an algorithm that is error-tolerant and orders of magnitude faster than existing symmetry-based algorithms. As an application, we rigorously characterize the stability of chimera states in networks with multiple types of interactions.

published version

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Cited by in corpus (15)

• Desynchronization transitions in adaptive networks
• Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions
• One-way dependent clusters and stability of cluster synchronization in directed networks
• Stability analysis of intralayer synchronization in time-varying multilayer networks with generic coupling functions
• Multistability and anomalies in oscillator models of lossy power grids
• Matryoshka and Disjoint Cluster Synchronization of Networks
• Synchronization scenarios in three-layer networks with a hub
• Collective dynamics on higher-order networks
• Symmetry-breaking mechanism for the formation of cluster chimera patterns
• Group synchrony, parameter mismatches, and intragroup connections
• Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks
• Cluster Synchronization via Graph Laplacian Eigenvectors
• Pinning control of networks: dimensionality reduction through simultaneous block-diagonalization of matrices
• Cluster Synchronization of Networks via a Canonical Transformation for Simultaneous Block Diagonalization of Matrices
• Optimal cost tuning of frustration: Achieving desired states in the Kuramoto-Sakaguchi model