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Alec Dunton

Picture of Alec Dunton.

Thesis

Topological Data Analysis for Systems of Coupled Oscillators

Advisor
Andrew J. Bernoff
Second Reader(s)
Chad M. Topaz (Macalester College)

Abstract

Coupled oscillators, such as groups of fireflies or clusters of neurons, are found throughout nature and are frequently modeled in the applied mathematics literature. Earlier work by Kuramoto, Strogatz, and others has led to a deep understanding of the emergent behavior of systems of such oscillators using traditional dynamical systems methods. In this project we outline the application of techniques from topological data analysis to understanding the dynamics of systems of coupled oscillators. This includes the examination of partitions, partial synchronization, and attractors. By looking for clustering in a data space consisting of the phase change of oscillators over a set of time delays we hope to reconstruct attractors and identify members of these clusters.

Additional Materials

Poster