2017/01/10 by Hongbin Chen, Yuting Sun, Jian Gao +2
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Ansatz #Applied mathematics #Astrophysics #Collective behavior #Combinatorics #Computer science #Kuramoto model #Mathematical physics #Mathematics #Network topology #Neural Networks Stability and Synchronization #Nonlinear Dynamics and Pattern Formation #Nonlinear system #Order (exchange) #Physics #Quantum mechanics #Slime Mold and Myxomycetes Research #Stability (learning theory) #Star (game theory) #Star network #Statistical physics #Synchronization (alternating current) #Synchronization networks #Topology (electrical circuits) #nlin.AO
paper · pdf · doi:10.1007/s11467-017-0651-4
published as Front. Phys. 12(6), 120504 (2017) · 10 pages, 7 figures
arxiv created 2017/01/10 · arxiv updated 2017/01/11 · openalex publication_date 2017/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical 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 the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.