A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow ...A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow a uniform probability density. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already reported 7r state and travelling wave state in the one with natural frequencies following Lorenztian probability density or a delta function. The dependence of the observed dynamics on the parameters of the model is explored and we find that the onset of synchronization in the model displays a non-monotonic dependence on both positive and negative coupling strength.展开更多
In this study we investigate the collective behavior of the generalized Kuramoto model with an ex- ternal pinning force in which oscillators with positive and negative coupling strengths are conformists and contrarian...In this study we investigate the collective behavior of the generalized Kuramoto model with an ex- ternal 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 oscilla- tors 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 contrar- ians oscillating around π periodically. In addition, we present the parameter space of the oscillating state and traveling wave state of the model.展开更多
基金Supported by National Natural Science Foundation of China under Grant No. 11247279
文摘A generalization of the Kuramoto model in which oscillators are coupled to the mean field with random signs is investigated in this work. We focus on a situation in which the natural frequencies of oscillators follow a uniform probability density. By numerically simulating the model, we find that the model supports a modulated travelling wave state except for already reported 7r state and travelling wave state in the one with natural frequencies following Lorenztian probability density or a delta function. The dependence of the observed dynamics on the parameters of the model is explored and we find that the onset of synchronization in the model displays a non-monotonic dependence on both positive and negative coupling strength.
基金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）.
文摘In this study we investigate the collective behavior of the generalized Kuramoto model with an ex- ternal 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 oscilla- tors 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 contrar- ians oscillating around π periodically. In addition, we present the parameter space of the oscillating state and traveling wave state of the model.
