论文标题
定期强迫库拉托托模型中的拓扑相变
Topological phase transition in the periodically forced Kuramoto model
论文作者
论文摘要
在[L. M. Childs和S. H. Strogatz。混乱18，043128（2008）]，识别模型中的所有分叉。我们表明，该分析预测的相图不完整。我们对方程式的数值分析表明，该模型还可以在增加场频率或降低磁场强度下突然从振荡到稳定参数的摇摆旋转。分叉分析未揭示这种过渡，因为它不是由分叉引起的，也不能被归类为第一阶或二阶，因为它没有显示任何两种过渡的关键现象特征。我们讨论了这种过渡的拓扑来源，并表明它是由订单参数空间中的单数点决定的。
A complete bifurcation analysis of explicit dynamical equations for the periodically forced Kuramoto model was performed in [L. M. Childs and S. H. Strogatz. Chaos 18 , 043128 (2008)], identifying all bifurcations within the model. We show that the phase diagram predicted by this analysis is incomplete. Our numerical analysis of the equations reveals that the model can also undergo an abrupt phase transition from oscillations to wobbly rotations of the order parameter under increasing field frequency or decreasing field strength. This transition was not revealed by bifurcation analysis because it is not caused by a bifurcation, and can neither be classified as first nor second-order since it does not display critical phenomena characteristic of either transition. We discuss the topological origin of this transition and show that it is determined by a singular point in the order-parameter space.
