Applied Mathematics Seminar-The synchronization problem for Kuramoto oscillators and beyond

Title: The synchronization problem for Kuramoto oscillators and beyond
Speaker: Javier Morales
Affiliation: University of Maryland
Date and Time: Friday, December 7, 11:10am-12:10pm
Place: Phillips 736

Abstract. Collective phenomena such as aggregation, flocking, and synchronization are ubiquitous in natural biological, chemical, and mechanical systems--e.g., the flashing of fireflies, chorusing of crickets, synchronous firing of cardiac pacemakers, and metabolic synchrony in yeast cell suspensions. The Kuramoto model introduced by  Yoshiki Kuramoto is one of the first theoretical tools developed to understand such phenomena and has recently gained extensive attention in the physical and mathematical community. Moreover, it has become the starting point of several generalizations that have applications ranging from opinion dynamics to the development of a human-made interacting multi-agent system of UAVs and data clustering. In this talk, we will review the state of the art for the synchronization problem of the Kuramoto model at the kinetic and particle level. Additionally, we will introduce new developments and variational techniques for the dynamics of this model and some of its variants and its generalization.