Department of Physics, East China Normal University, Shanghai 200241, China.
Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China.
Phys Rev E. 2019 Nov;100(5-1):052310. doi: 10.1103/PhysRevE.100.052310.
For decades, the description and characterization of nonstationary coherent states in coupled oscillators have not been available. We here consider the Kuramoto model consisting of conformist and contrarian oscillators. In the model, contrarians are chosen from a bimodal Lorentzian frequency distribution and flipped into conformists at random. A complete and systematic analytical treatment of the model is provided based on the Ott-Antonsen ansatz. In particular, we predict and analyze not only the stability of all stationary states (such as the incoherent, the π, and the traveling-wave states), but also that of the two nonstationary states: the Bellerophon and the oscillating-π state. The theoretical predictions are fully supported by extensive numerical simulations.
几十年来，关于耦合振荡器中非平稳相干态的描述和特征一直无法获得。在这里，我们考虑由从众和逆反振荡器组成的 Kuramoto 模型。在该模型中，逆反者是从双峰 Lorentzian 频率分布中选择出来的，并随机翻转成从众者。基于 Ott-Antonsen 假设，我们对该模型提供了完整而系统的分析处理。特别地，我们不仅预测和分析了所有稳定态（如非相干态、π 态和行波态）的稳定性，还预测和分析了两个非稳定态：Bellerophon 态和振荡-π 态的稳定性。理论预测得到了广泛的数值模拟的完全支持。
