Network-complement transitions, symmetries, and cluster synchronization
arXiv:1712.06613 · doi:10.1063/1.4960617
Abstract
Synchronization in networks of coupled oscillators is known to be largely determined by the spectral and symmetry properties of the interaction network. Here we leverage this relation to study a class of networks for which the threshold coupling strength for global synchronization is the lowest among all networks with the same number of nodes and links. These networks, defined as being uniform, complete, and multi-partite (UCM), appear at each of an infinite sequence of network-complement transitions in a larger class of networks characterized by having near-optimal thresholds for global synchronization. We show that the distinct symmetry structure of the UCM networks, which by design are optimized for global synchronizability, often leads to formation of clusters of synchronous oscillators, and that such states can coexist with the state of global synchronization.
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References in corpus (28)
- Critical phenomena in complex networks
- Chimera States for Coupled Oscillators
- Explosive Synchronization Transitions in Scale-free Networks
- Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
- Network Synchronization, Diffusion, and the Paradox of Heterogeneity
- Turing patterns in network-organized activator-inhibitor systems
- Turing patterns on networks
- Synchronization on small-world networks
- Entangled networks, synchronization, and optimal network topology
- Zero-lag long-range synchronization via dynamical relaying
- Enhancing complex-network synchronization
- "Explosive Percolation" Transition is Actually Continuous
- Remote synchronization reveals network symmetries and functional modules
- Synchronization is optimal in non-diagonalizable networks
- Complete Characterization of Stability of Cluster Synchronization in Complex Dynamical Networks
- Frequency synchronization in random oscillator network
- Cluster and group synchronization in delay-coupled networks
- Impact of Single Links in Competitive Percolation -- How complex networks grow under competition
- Self-organized adaptation of a simple neural circuit enables complex robot behaviour
- On Automorphism Groups of Networks
- Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions
- Cluster Explosive Synchronization in Complex Networks
- Explosive Percolation: Novel critical and supercritical phenomena
- Maximum Performance at Minimum Cost in Network Synchronization
- Analysis of Remote Synchronization in Complex Networks
- The emergence of coherence in complex networks of heterogeneous dynamical systems
- Controlling synchronous patterns in complex networks
- Optimal Synchronization in Space
Cited by in corpus (6)
- Exploiting symmetry in network analysis
- Introduction to Focus Issue: Patterns of Network Synchronization
- Does the brain behave like a (complex) network? I. Dynamics
- Cluster synchronization in complex network of coupled chaotic circuits: an experimental study
- Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators
- Characterizing correlations and synchronization in collective dynamics