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Nontrivial standing wave state in frequency-weighted Kuramoto model

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Abstract

Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two first-order transitions in both the forward and backward directions. Apart from the trivial phase-locked state, a novel nonstationary coherent state, i.e., a nontrivial standing wave state is observed and characterized. In this state, oscillators inside the coherent clusters are not frequency-locked as they would be in the usual standing wave state. Instead, their average frequencies are locked to a constant. The critical coupling strength from the incoherent state to the nontrivial standing wave state can be obtained by performing linear stability analysis. The theoretical results are supported by the numerical simulations.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China under Grant No. 11135001.

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Authors and Affiliations

  1. Department of Physics, East China Normal University, Shanghai, 200241, China

    Hong-Jie Bi, Yan Li & Shu-Guang Guan

  2. Nantong Middle School, 9 Zhongxuetang Road, Nantong, 226001, China

    Yan Li

  3. No. 4 Middle School Affiliated to ECNU, 279 Luding Road, Shanghai, 200062, China

    Li Zhou

Authors
  1. Hong-Jie Bi
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  2. Yan Li
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  3. Li Zhou
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  4. Shu-Guang Guan
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Corresponding authors

Correspondence to Li Zhou or Shu-Guang Guan.

Additional information

These authors contributed equally to this work. arXiv: 1702.08629.

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Bi, HJ., Li, Y., Zhou, L. et al. Nontrivial standing wave state in frequency-weighted Kuramoto model. Front. Phys. 12, 126801 (2017). https://doi.org/10.1007/s11467-017-0672-z

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  • DOI: https://doi.org/10.1007/s11467-017-0672-z

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