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arXiv · 1701.02592

Order parameter analysis of synchronization transitions on star networks

Hongbin Chen·Yuting Sun·Jian Gao·Can Xu·Zhigang Zheng
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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.

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Hongbin Chen, Yuting Sun, Jian Gao, Can Xu, Zhigang Zheng. 2017-01-10. Order parameter analysis of synchronization transitions on star networks. https://doi.org/10.1007/s11467-017-0651-4

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