Symmetry- and Input-Cluster Synchronization in Networks
arXiv:1804.01462 · doi:10.1103/PhysRevE.97.042217
Abstract
We study cluster synchronization in networks and show that the stability of all possible cluster synchronization patterns depends on a small set of Lyapunov exponents. Our approach can be applied to clusters corresponding to both orbital partitions of the network nodes (symmetry-cluster synchronization) and equitable partitions of the network nodes (input-cluster synchronization.) Our results are verified experimentally in networks of coupled opto-electronic oscillators.
arXiv comment19 pages, 8 figures
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- Exploiting symmetry in network analysis
- Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
- Symmetry-independent stability analysis of synchronization patterns
- One-way dependent clusters and stability of cluster synchronization in directed networks
- Identifying symmetries and predicting cluster synchronization in complex networks
- Matryoshka and Disjoint Cluster Synchronization of Networks
- Modal Decomposition of the Linear Swing Equation in Networks with Symmetries
- Decoupled synchronized states in networks of linearly coupled limit cycle oscillators
- Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks
- Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies
- Emergence of chaotic cluster synchronization in heterogeneous networks
- Detecting partial synchrony in a complex oscillatory network using pseudo-vortices
- Cluster Synchronization of Networks via a Canonical Transformation for Simultaneous Block Diagonalization of Matrices
- Comment on "Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks"