Existence of solutions to the infinite dimensional Kuramoto model

dc.contributor.advisor Leander, Rachel N
dc.contributor.author Krueger, Anthony Raymond
dc.contributor.committeemember Ding, Wandi
dc.contributor.committeemember Sinkala, Zachariah
dc.contributor.committeemember Hart, James
dc.contributor.committeemember Wu, Yixiang
dc.contributor.committeemember Robertson, William
dc.date.accessioned 2021-04-23T01:01:49Z
dc.date.available 2021-04-23T01:01:49Z
dc.date.issued 2021
dc.date.updated 2021-04-23T01:01:50Z
dc.description.abstract The Kuramoto model is a kinetic model of phase-coupled oscillators. This model has a long legacy, starting from Kuramoto's text, \textit{Oscillations, Waves, and Turbulence}, which provided the foundation and initial analysis of the model. Kuramoto defined convenient measures of the average phase and variance to describe the population's macroscopic state. Since Kuramoto's original publication, researchers have worked to better characterize solution dynamics. In a much-cited paper, Ott and Antonsen showed that in some cases solutions adhere to a convenient ansatz, which greatly simplifies model analysis. Here we combine the method of characteristics with an iterative technique to prove existence and uniqueness of solutions to the infinite dimensional Kuramoto model. Our result differs from the result of Ott and Antonsen in that we require the initial data is twice continuously differentiable and show existence of continuously differentiable solutions, whereas the ansatz of Ott and Antonsen requires the solution and initial data are twice continuously differentiable and belong to a special class of Fourier series. We believe the alternative approach to model analysis developed here has the potential to open doors to future results on the extensively studied Kuramoto model.
dc.description.degree M.S.
dc.identifier.uri https://jewlscholar.mtsu.edu/handle/mtsu/6419
dc.language.rfc3066 en
dc.publisher Middle Tennessee State University
dc.source.uri http://dissertations.umi.com/mtsu:11366
dc.subject Analysis
dc.subject Kuramoto
dc.subject Method of Characteristics
dc.subject Oscillator
dc.subject PDE
dc.subject Synchronicity
dc.subject Mathematics
dc.thesis.degreelevel masters
dc.title Existence of solutions to the infinite dimensional Kuramoto model
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