Order parameter analysis of synchronization transitions on star networks
arXiv:1701.02592 · doi:10.1007/s11467-017-0651-4
Abstract
Collective behaviors of populations of coupled oscillators have attracted much attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynam- ical mechanism of collective synchronizations by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe-Strogatz transformation, Ott-Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to diverse col- lective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions are revealed in the star-network model by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.
10 pages, 7 figures
References in corpus (6)
- Synchronization in complex networks
- Critical phenomena in complex networks
- Low Dimensional Behavior of Large Systems of Globally Coupled Oscillators
- Explosive Synchronization Transitions in Scale-free Networks
- Explosive first-order transition to synchrony in networked chaotic oscillators
- Invariant submanifold for series arrays of Josephson junctions