Periodic synchronization in a system of coupled phase oscillators with attractive and repulsive interactions |
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| Authors: | Di Yuan Jun-Long Tian Fang Lin Dong-Wei Ma Jing Zhang Hai-Tao Cui Yi Xiao |
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| Affiliation: | 1. School of Physics and Electrical Engineering, Anyang Normal University, Anyang 455000, China2. School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China |
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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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| Keywords: | generalized Kuramoto model pinning force conformists contrarians oscillating π state |
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