Synchronization in Networks with Higher Order Interactions

同步在生物、工程和物理系统中普遍存在。同步的例子包括电网中的交流电、脑节律、昼夜节律和激光。传统上，同步的研究是假设振荡系统成对地相互作用。然而，在许多情况下，这些系统以三个或更多个为一组进行交互。本计画将研究群互动系统中的同步。除了推进对同步过程的基本理解外，本项目中开发的理论和技术将促进同步模式的预测和控制，在许多科学和工程领域具有潜在的益处。该研究项目将提供一个机会，培养研究生对复杂和跨学科的动力系统建模。 研究结果将通过在期刊上发表和在会议上介绍的方式传播。定期为高年级本科生和研究生开设网络动力学课程，为对网络动力学感兴趣的学生提供凝聚力。 用网络来描述复杂系统是非常成功的。把一个复杂系统描述为一个网络，是假设主体之间的相互作用是成对的。然而，在一些重要的情况下，交互作用同时包含多个单元。这样的系统可以被描述为超图，超图是网络的一种概括，其中可以在两个以上的单元之间发生交互。本计画将研究编码振子耦合的超图的结构如何决定振子的同步。虽然人们知道，组的相互作用可以修改一些简单的超图同步过程的动力学，超图结构对同步的全面影响还没有得到很好的理解。这项工作将填补这一空白，发展一个全面和广泛的框架来研究超图中的振荡器同步。一个理论框架，可以解释不同的超图结构，振荡器的相互作用类型，以及它们之间的相关性将被开发。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Synchronization is pervasive in biological, engineered, and physical systems. Examples of synchronization include alternating current in power grids, brain rhythms, circadian rhythms, and lasers. Traditionally, synchronization has been studied by assuming that the oscillating systems interact in pairs. However, in many situations these systems interact in groups of three or more. This project will study synchronization in systems with group interactions. In addition to advancing basic understanding of synchronization processes, the theories and techniques developed in this project will facilitate prediction and control of synchronization patterns with potential benefits in many areas of science and engineering. The research project will provide an opportunity to train a graduate student on modeling complex and interdisciplinary dynamical systems. The research results will be disseminated by publication in journals and presentation in conferences. A class on dynamics on networks for advanced undergraduate and graduate students will be taught regularly, providing a coalescing force for the students interested in dynamics on networks. The description of complex systems in terms of networks has been extremely successful. Describing a complex system as a network assumes that interactions between agents are only pairwise. However, there are important cases where interactions encompass multiple units simultaneously. Such systems can be described as hypergraphs, a generalization of a network where interactions can occur between more than two units. This project will study how the structure of the hypergraph that encodes oscillator coupling determines the synchronization of the oscillators. While it is known that group interactions can modify the dynamics of synchronization processes for some simple hypergraphs, the full effect of hypergraph structure on synchronization is not well understood yet. This work will fill this gap by developing a comprehensive and broad framework to study synchronization of oscillators in hypergraphs. A theoretical framework that can account for different hypergraph structures, oscillator interaction types, and correlations between them will be developed. The approach is based on the use of appropriate hypergraph generative models and dimensional reduction techniques.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.