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The Ott–Antonsen Ansatz in Globally Coupled Phase Oscillators |
| Nian-Ping Wu, Hong-Yan Cheng, Qiong-Lin Dai, Hai-Hong Li** |
School of Sciences, Beijing University of Posts and Telecommunications, Beijing 100876
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| Cite this article: |
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Nian-Ping Wu, Hong-Yan Cheng, Qiong-Lin Dai et al 2016 Chin. Phys. Lett. 33 070501 |
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Abstract The Ott–Antonsen ansatz provides a powerful tool in investigating synchronization among coupled phase oscillators. However, previous works using the ansatz only focused on the evolution of the order parameter and the information on desynchronized oscillators is less discussed. In this work, we show that the Ott–Antonsen ansatz can also be applied to investigate the desynchronous dynamics in coupled phase oscillators. Studying the original Kuramoto model and two of its variants, we find that the dynamics of $\alpha(\omega)$, the coefficient in the Fourier series of the probability density, can give most of the information on the synchronization, for example, the threshold of natural frequency delimiting the oscillators synchronized and desychronized by the mean field, the formulation of the effective frequency $\omega_{\rm e}(\omega)$ of desynchronous oscillators, and the structure of the graph $\omega_{\rm e}(\omega)$.
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Received: 07 March 2016
Published: 01 August 2016
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| PACS: |
05.45.Xt
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(Synchronization; coupled oscillators)
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43.40.At
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(Experimental and theoretical studies of vibrating systems)
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36.40.Ei
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(Phase transitions in clusters)
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