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Applied Math Colloquium

Friday, February 21, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Complex Collective Dynamics in Networks of Phase Oscillators

Paul So

George Mason University

Abstract

In nature and in many practical applications, it is not uncommon to observe the emergence of coherent macroscopic behavior in large populations of interacting rhythmic units despite noise and the presence of heterogeneity in the population. Through a recently developed analytical method, the asymptotic macroscopic dynamics for a class of globally coupled phase oscillators including the emblematic Kuramoto system, a collection of canonical Type-I neurons, and arrays of over-damped Josephson junctions, were analyzed through a set of derived low-dimensional mean field equations. This talk describes some of the basic macroscopic states and their bifurcations. Interestingly, these large networks of simple phase oscillators can support a macroscopic chaotic state and other complex collective dynamics. Lastly, through a global network parameter, we demonstrated that these complex macroscopic patterns can be controlled using a feedback controller constructed from the derived mean field dynamics.