Stable Chimeras and Independently Synchronizable Clusters

Abstract

Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we establish a theoretical basis to divide an arbitrary pattern of symmetry clusters into independently synchronizable cluster sets, in which the synchronization stability of the individual clusters in each set is decoupled from that in all the other sets. Using this framework, we suggest a new approach to find permanently stable chimera states by capturing two or more symmetry clusters---at least one stable and one unstable---that compose the entire fully symmetric network.

Proof corrections implemented; 5 pages, 3 figures [+ Supplemental Material (15 pages, 7 figures)]; Software for grouping synchronization clusters downloadable from https://github.com/tnishi0/grouping-clusters

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Cited by in corpus (15)

• Symmetries and Cluster Synchronization in Multilayer Networks
• Topological Control of Synchronization Patterns: Trading Symmetry for Stability
• Connecting the Kuramoto Model and the Chimera State
• One-way dependent clusters and stability of cluster synchronization in directed networks
• Mechanism for Strong Chimeras
• Critical Switching in Globally Attractive Chimeras
• Modal Decomposition of the Linear Swing Equation in Networks with Symmetries
• Impact of intra and inter-cluster coupling balance on the performance of nonlinear networked systems
• Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies
• Analyzing states beyond full synchronization on hypergraphs requires methods beyond projected networks
• Concurrent formation of nearly synchronous clusters in each intertwined cluster set with parameter mismatches
• Pinning control of networks: dimensionality reduction through simultaneous block-diagonalization of matrices
• Approximate Network Symmetry
• Comment on "Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks"
• Chimera dynamics in nonlocally coupled moving phase oscillators