Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi'an 710072, China.
School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China.
Phys Rev Lett. 2020 Nov 6;125(19):194101. doi: 10.1103/PhysRevLett.125.194101.
From fireflies to cardiac cells, synchronization governs important aspects of nature, and the Kuramoto model is the staple for research in this area. We show that generalizing the model to oscillators of dimensions higher than 2 and introducing a positive feedback mechanism between the coupling and the global order parameter leads to a rich and novel scenario: the synchronization transition is explosive at all even dimensions, whilst it is mediated by a time-dependent, rhythmic, state at all odd dimensions. Such a latter circumstance, in particular, differs from all other time-dependent states observed so far in the model. We provide the analytic description of this novel state, which is fully corroborated by numerical calculations. Our results can, therefore, help untangle secrets of observed time-dependent swarming and flocking dynamics that unfold in three dimensions, and where this novel state could thus provide a fresh perspective for as yet not understood formations.
从萤火虫到心肌细胞，同步现象控制着自然界的许多重要方面，而 Kuramoto 模型则是该领域研究的基础。我们证明，将模型推广到维度高于 2 的振荡器，并在耦合和全局序参量之间引入正反馈机制，会导致一个丰富而新颖的场景：在所有偶数维度上，同步相变是爆炸式的，而在所有奇数维度上，它是通过一个时变的、有节奏的状态来介导的。特别是这种后一种情况，与迄今为止在该模型中观察到的所有其他时变状态都不同。我们提供了对这种新状态的分析描述，这一描述得到了数值计算的充分证实。因此，我们的结果可以帮助揭示在三维空间中展开的观察到的时变群体和集群动力学的秘密，而这种新状态可能为尚未理解的群体提供一个新的视角。
