Synchronization in Networks with Higher Order Interactions

University Of Colorado At Boulder, Boulder CO

Investigators

Abstract

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.