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Periodic synchronization in a system of coupled phase oscillators with attractive and repulsive interactions

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Abstract

In this study we investigate the collective behavior of the generalized Kuramoto model with an external pinning force in which oscillators with positive and negative coupling strengths are conformists and contrarians, respectively. We focus on a situation in which the natural frequencies of the oscillators follow a uniform probability density. By numerically simulating the model, it is shown that the model supports multistable synchronized states such as a traveling wave state, π state and periodic synchronous state: an oscillating π state. The oscillating π state may be characterized by the phase distribution oscillating in a confined region and the phase difference between conformists and contrarians oscillating around π periodically. In addition, we present the parameter space of the oscillating π state and traveling wave state of the model.

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Acknowledgements

The work was supported by the National Natural Science Foundation of China (Grant Nos. 11447001, 11475004, and U1504108), the Key Project of Scientific and Technological Research of the Education Department of Henan Province (Grant Nos. 16A140002, 18A140012, and 18B140001), and the Innovation Foundation for Students of Anyang Normal University (Grant No. ASCX/2017-Z59).

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Correspondence to Di Yuan or Jun-Long Tian.

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Yuan, D., Tian, JL., Lin, F. et al. Periodic synchronization in a system of coupled phase oscillators with attractive and repulsive interactions. Front. Phys. 13, 130504 (2018). https://doi.org/10.1007/s11467-018-0748-4

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  • DOI: https://doi.org/10.1007/s11467-018-0748-4

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