发表机构
RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences (iTHEMS); Department of Systems and Control Engineering, Institute of Science Tokyo; Research Center for Autonomous Systems Materialogy, Institute of Science Tokyo; Department of Mathematics, Vrije Universiteit Amsterdam; Institute for Advanced Study, Technical University of Munich; Department of Mathematics, University of Exeter; Mathematical Institute, University of Oxford（RIKEN跨学科理论与数学科学中心(iTHEMS); 东京科学大学系统控制工程学院; 东京科学大学自主系统材料学研究中心; 阿姆斯特丹自由大学数学系; 慕尼黑工业大学高等研究院; 埃克塞特大学数学系; 牛津大学数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用参数化方法进行高阶相位约化，区分物理与涌现非成对相互作用，并通过网络模体设计耦合，为同步工程应用开辟新途径。
AI 中文摘要
相位约化是一种从高维振荡系统获得相位模型的强大技术。从成对相互作用出发，一阶近似产生Kuramoto和Winfree相位模型，而非成对相互作用在二阶出现。近期，相位模型已被扩展以考虑非成对相互作用，特别是高阶Kuramoto模型。物理非成对相互作用与涌现非成对相互作用之间是否存在内在差异？我们能否利用前者来平衡后者的效应？在本工作中，我们利用一种最近发展的参数化方法计算相位约化并回答这些问题。在将新方法与经典Kuramoto式相位约化进行比较后，我们求解了涌现非成对相互作用的网络模体，并将其与物理模体进行比较。最后，我们利用这些模体采用一种耦合设计方法。我们的框架为在同步工程应用中进一步利用物理非成对相互作用铺平了道路。
英文摘要
Phase reduction is a powerful technique to obtain phase models from highly dimensional oscillatory systems. Starting from pairwise interactions, a first order approximation yields Kuramoto and Winfree phase models, while nonpairwise interactions emerge at the second order. Recently, phase models have been extended to account for nonpairwise interactions, notably, the higher-order Kuramoto model. Is there an intrinsic difference between physical and emergent nonpairwise interactions? And can we make use of the former to even out the effects of the latter? In this work, we exploit a recently developed parametrization method to compute the phase reduction and answer these questions. After a comparison of the new method with the classic Kuramoto-style phase reduction, we solve the network motifs of the emergent nonpairwise interactions and compare them with the physical once. Lastly, we exploit the motifs to adopt a coupling design approach. Our framework paves the way for further exploitations of physical nonpairwise interactions for applications in synchronization engineering.
