Synchronization in Networks with Higher Order Interactions

具有高阶交互的网络同步

• 批准号: 2205967
• 负责人: Juan Restrepo
• 金额: $ 25万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-09-01 至 2025-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2205967&HistoricalAwards=false
• 关键词: Synchronization; Networks; Higher; Order; Interactions

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.

同步在生物，工程和物理系统中普遍存在。同步的示例包括电网，脑部节奏，昼夜节律和激光的交替电流。传统上，通过假设振荡系统成对相互作用来研究同步。但是，在许多情况下，这些系统分为三个或更多。该项目将研究具有组相互作用的系统中的同步。除了促进对同步过程的基本理解外，该项目中开发的理论和技术还将促进对同步模式的预测和控制，这些模式在科学和工程的许多领域都具有潜在的好处。该研究项目将为培训研究生建模复杂和跨学科动力学系统的机会提供机会。 研究结果将通过期刊和会议上的介绍中的出版物传播。将定期教授有关高级本科生和研究生网络动力学的课程，为对网络动态感兴趣的学生提供联合力量。 在网络方面对复杂系统的描述非常成功。将复杂的系统描述为网络，假设代理之间的相互作用仅成对。但是，在某些重要情况下，相互作用同时包含多个单元。这样的系统可以描述为超图，这是一个网络的概括，其中可以在两个以上单位之间进行交互。该项目将研究编码振荡器耦合的超图的结构如何决定振荡器的同步。虽然众所周知，组相互作用可以修改一些简单的超图的同步过程的动力学，但尚不清楚超图结构对同步的全部影响。这项工作将通过开发一个全面而广泛的框架来研究超图中振荡器的同步。可以解释不同的超图结构，振荡器相互作用类型以及它们之间的相关性的理论框架。该方法是基于使用适当的超图生成模型和尺寸缩小技术的使用。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛的影响审查标准通过评估来支持的。

项目成果

Synchronization of phase oscillators on complex hypergraphs

• DOI: 10.1063/5.0116747
• 发表时间: 2023-03-01
• 期刊: CHAOS
• 影响因子: 2.9
• 作者: Adhikari, Sabina;Restrepo, Juan G. G.;Skardal, Per Sebastian
• 通讯作者: Skardal, Per Sebastian