Topological synchronization of coupled nonlinear oscillators
Topological synchronization of coupled nonlinear oscillators
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DOI：
10.1103/physrevresearch.4.023211
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发表时间：
2020-12
影响因子：
4.2
通讯作者：
K. Sone;Yuto Ashida;T. Sagawa
中科院分区：
文献类型：
--
作者：
K. Sone;Yuto Ashida;T. Sagawa
耦合振荡器的同步是自然界中普遍存在的现象。它的鲁棒性实现对于我们理解从生物功能到电气工程等各种非线性系统至关重要。在另一方面，在凝聚态物理中，拓扑学被用来实现像拓扑边缘模式这样的鲁棒性，正如著名的拓扑绝缘体所证明的那样。在这里，我们将这两种研究方法结合起来，提出了一种非线性拓扑现象，即拓扑同步，即只有边缘振子同步，而大块振子表现出混沌动力学。我们分析了一个具体的原型模型，证明了正Lyapunov指数和沿边缘局部化的Lyapunov向量的存在。作为非线性系统拓扑的一个独特特征，我们发现在新出现的有效边界处出现了非常规的额外拓扑边界模式。此外，我们的建议显示了空间控制同步的希望，如按需模式形成和缺陷检测。拓扑同步可以普遍出现在拓扑非线性振荡器中，从而为实现鲁棒性、几何性和灵活性的同步提供了指导原则。
Synchronization of coupled oscillators is a ubiquitous phenomenon found throughout nature. Its robust realization is crucial to our understanding of various nonlinear systems, ranging from biological functions to electrical engineering. On another front, in condensed matter physics, topology is utilized to realize robust properties like topological edge modes, as demonstrated by celebrated topological insulators. Here, we integrate these two research avenues and propose a nonlinear topological phenomenon, namely topological synchronization, where only the edge oscillators synchronize while the bulk ones exhibit chaotic dynamics. We analyze a concrete prototypical model to demonstrate the presence of positive Lyapunov exponents and Lyapunov vectors localized along the edge. As a unique characteristic of topology in nonlinear systems, we find that unconventional extra topological boundary modes appear at emerging effective boundaries. Furthermore, our proposal shows promise for spatially controlling synchronization, such as on-demand pattern formation and defect detection. The topological synchronization can ubiquitously appear in topological nonlinear oscillators and thus can provide a guiding principle to realize synchronization in a robust, geometrical, and flexible way.