Topological Control of Synchronization Patterns: Trading Symmetry for Stability
arXiv:1902.03255 · doi:10.1103/PhysRevLett.122.058301
Abstract
Symmetries are ubiquitous in network systems and have profound impacts on the observable dynamics. At the most fundamental level, many synchronization patterns are induced by underlying network symmetry, and a high degree of symmetry is believed to enhance the stability of identical synchronization. Yet, here we show that the synchronizability of almost any symmetry cluster in a network of identical nodes can be enhanced precisely by breaking its structural symmetry. This counterintuitive effect holds for generic node dynamics and arbitrary network structure and is, moreover, robust against noise and imperfections typical of real systems, which we demonstrate by implementing a state-of-the-art optoelectronic experiment. These results lead to new possibilities for the topological control of synchronization patterns, which we substantiate by presenting an algorithm that optimizes the structure of individual clusters under various constraints.
arXiv comment6 pages, 2 figures, plus Supplemental Materials
References in corpus (23)
- Synchronization in small-world systems
- Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?
- Symmetries, Cluster Synchronization, and Isolated Desynchronization in Complex Networks
- Entangled networks, synchronization, and optimal network topology
- 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
- On Automorphism Groups of Networks
- Network synchronization landscape reveals compensatory structures, quantization, and the positive effect of negative interactions
- Observability and Controllability of Nonlinear Networks: The Role of Symmetry
- Experimental observation of chimera and cluster states in a minimal globally coupled network
- Synchronizing distant nodes: a universal classification of networks
- Maximum Performance at Minimum Cost in Network Synchronization
- Experimental Observations of Group Synchrony in a System of Chaotic Optoelectronic Oscillators
- Symmetric States Requiring System Asymmetry
- Stable Chimeras and Independently Synchronizable Clusters
- Controlling synchronization in large laser networks using number theory
- Control of synchronization patterns in neural-like Boolean networks
- Breaking Synchrony by Heterogeneity in Complex Networks
- Asymmetry-Induced Synchronization in Oscillator Networks
- Experiments with arbitrary networks in time-multiplexed delay systems
- Identical synchronization of nonidentical oscillators: when only birds of different feathers flock together
- Synchronization with mismatched synaptic delays: A unique role of elastic neuronal latency
Cited by in corpus (25)
- Data-Driven Control of Complex Networks
- Asymmetric balance in symmetry breaking
- Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions
- Delayed Dynamical Systems: Networks, Chimeras and Reservoir Computing
- Enhanced stability, bistability, and exceptional points in saturable active photonic couplers
- Koopman Operator and its Approximations for Systems with Symmetries
- Does the brain behave like a (complex) network? I. Dynamics
- Mechanism for Strong Chimeras
- Critical Switching in Globally Attractive Chimeras
- Dirac synchronization is rhythmic and explosive
- Local Dirac Synchronization on Networks
- Asymmetry-induced order in multilayer networks
- Phase-Amplitude Coupling in Neuronal Oscillator Networks
- Eigenvector-based analysis of cluster synchronization in general complex networks of coupled chaotic oscillators
- Revealing dynamics, communities and criticality from data
- Heterogeneity-stabilized homogeneous states in driven media
- Solitary states in complex networks: impact of topology
- Estimating the master stability function from the time series of one oscillator via reservoir computing
- Frequency Synchronization Induced by Frequency Detuning
- Forget Partitions: Cluster Synchronization in Directed Networks Generate Hierarchies
- Interpretable disorder-promoted synchronization and coherence in coupled laser networks
- Robust reconstruction of sparse network dynamics
- Designing topological cluster synchronization patterns with the Dirac operator
- Comment on "Failure of the simultaneous block diagonalization technique applied to complete and cluster synchronization of random networks"
- Controlling symmetries and clustered dynamics of complex networks