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Applied Mathematics Colloquium

Friday, September 7, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

A Kinetic Theory for Coupled Oscillators

Carson Chow

Laboratory of Biological Modeling

National Institutes of Health

Bethesda, MD

Abstract

Networks of coupled oscillators have been used to model a wide range of phenomena such as interacting neurons, flashing fireflies, chirping crickets and coupled Josephson junctions. Typically, these networks have been studied analytically when the number of oscillators are small or in the "mean field" infinite size limit. The dynamics of networks that are large but not infinite is not well understood, although this is a regime where many of the interesting applications lie. I will present a formalism to analyze large but finite-sized networks using an approach borrowed from the kinetic theory of plasmas and gases. The result is a BBGKY-like moment hierarchy that can be truncated to estimate finite-sized fluctuation and correlation effects. In addition, it can be shown that the moment hierarchy is equivalent to a path integral formulation where diagrammatic methods can be employed to assist in the analytical calculations.