Kuramoto模型中的非标准跃迁：不对称性在固有频率分布中的作用
Nonstandard transitions in the Kuramoto model: A role of asymmetry in natural frequency distributions
摘要：
我们研究仓本模型中的过渡，通过揭示固有频率分布的不对称性，这在以前的许多研究中被假设为对称的。这种不对称性在双峰性的帮助下产生了两个非标准的分岔图。第一个图由稳态组成，并且随着耦合强度的增加，具有标准的连续同步过渡和随后的不连续过渡。这样的分叉图也被报道在一个变体模型，它打破了奇对称的耦合函数引入相位滞后。第二个图包括从部分同步状态出现的振荡状态，然后是不连续的过渡。该图是本研究首次揭示的。通过直接的$N$ -体模拟，验证了这两个分岔图的正确性。我们的结论是，分布的不对称性，双峰，发挥了类似的作用，相位滞后，并多样化的过渡。
英文摘要：
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.
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