A universal order parameter for synchrony in networks of limit cycle oscillators
arXiv:1704.04130 · doi:10.1063/1.4995963
Abstract
We analyze the properties of order parameters measuring synchronization and phase locking in complex oscillator networks. First, we review network order parameters previously introduced and reveal several shortcomings: none of the introduced order parameters capture all transitions from incoherence over phase locking to full synchrony for arbitrary, finite networks. We then introduce an alternative, universal order parameter that accurately tracks the degree of partial phase locking and synchronization, adapting the traditional definition to account for the network topology and its influence on the phase coherence of the oscillators. We rigorously proof that this order parameter is strictly monotonously increasing with the coupling strength in the phase locked state, directly reflecting the dynamic stability of the network. Furthermore, it indicates the onset of full phase locking by a diverging slope at the critical coupling strength. The order parameter may find applications across systems where different types of synchrony are possible, including biological networks and power grids.
8 pages, 4 figures
References in corpus (6)
- Synchronization in complex networks
- Paths to Synchronization on Complex Networks
- Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
- Erosion of synchronization in networks of coupled oscillators
- Cycle flows and multistabilty in oscillatory networks: an overview
- Does dynamics reflect topology in directed networks?
Cited by in corpus (16)
- What adaptive neuronal networks teach us about power grids
- Stability and control of power grids with diluted network topology
- Effect of disorder and noise in shaping the dynamics of power grids
- Enhancing synchronization by optimal correlated noise
- Threefold way to the dimension reduction of dynamics on networks: an application to synchronization
- Self-consistent Method and Steady States of Second-order Oscillators
- Effects of Synaptic and Myelin Plasticity on Learning in a Network of Kuramoto Phase Oscillators
- Synchronization dynamics on the EU and US power grids
- Qualitative Stability and Synchronicity Analysis of Power Network Models in Port-Hamiltonian Form
- Synchronization transitions on connectome graphs with external force
- Chimera states in neural networks and power systems
- Improving power-grid systems via topological changes, or how self-organized criticality can help stability
- Dynamics of oscillator populations with disorder in the coupling phase shifts
- Dynamical heterogeneity and universality of power-grids
- Studying power-grid synchronization with incremental refinement of model heterogeneity
- The effect of HVDC lines in power-grids via Kuramoto modelling