Nonstandard transitions in the Kuramoto model: a role of asymmetry in natural frequency distributions
Nonstandard transitions in the Kuramoto model: a role of asymmetry in natural frequency distributions
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DOI：
10.1088/1742-5468/aa53f6
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发表时间：
2016-09
期刊：
影响因子：
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通讯作者：
Yu Terada;Keigo Ito;T. Aoyagi;Y. Yamaguchi
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作者：
Yu Terada;Keigo Ito;T. Aoyagi;Y. Yamaguchi
我们通过揭示自然频率分布的不对称性来研究Kuramoto模型中的相变，在许多以前的研究中，自然频率分布被假设为对称的。这种不对称性产生了两个非标准分叉图，借助于双峰性。第一个图由定态组成，随着耦合强度的增加，有标准的连续同步跃迁和随后的不连续跃迁。这样的分岔图在一种不同的模型中也有报道，它通过引入相位滞后打破了耦合函数的奇对称性。第二张图包括从部分同步状态出现的振荡状态，然后是不连续的转变。这张图是在这项研究中首次发现的。利用Ott-Antonsen ansatz方法得到了这两种分叉图，并用直接N体仿真进行了验证。我们得出的结论是，分布的不对称性具有双峰性，其作用类似于位相滞后，并使相变多样化。
We study transitions in the Kuramoto model by shedding light on asymmetry in the natural frequency distribution, which has been assumed to be symmetric in many previous studies. The asymmetry brings two nonstandard bifurcation diagrams, with the aid of bimodality. The first diagram consists of stationary states, and has the standard continuous synchronization transition and a subsequent discontinuous transition as the coupling strength increases. Such a bifurcation diagram has been also reported in a variant model, which breaks the odd symmetry of the coupling function by introducing the phase lag. The second diagram includes the oscillatory state emerging from the partially synchronized state and followed by a discontinuous transition. This diagram is firstly revealed in this study. The two bifurcation diagrams are obtained by employing the Ott–Antonsen ansatz, and are verified by direct N-body simulations. We conclude that the asymmetry in distribution, with the bimodality, plays a similar role to the phase lag, and diversifies the transitions.