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Existence, Uniqueness, and Stability of Traveling Waves in Neural Field Models

About this Digital Document

We study the existence, uniqueness, and stability of traveling waves in neural field models under various assumptions on the firing rates and kernels. In the case of Heaviside ring rates, we study unique fronts arising from oscillatory synaptic coupling types. We then use functional analysis to show that Heaviside firing rates can be continuously deformed into smooth, sigmoidal functions and the existence of fronts persists. Finally, we combine our results for the front with geometric singular perturbation theory to prove the existence of pulses when certain lateral inhibition kernels reduce the systems of integral equations into systems of PDEs.
Full Title
Existence, Uniqueness, and Stability of Traveling Waves in Neural Field Models
Contributor(s)
Creator: Dyson, Alan
Thesis advisor: Zhang, Linghai
Publisher
Lehigh University
Date Issued
2019-01
Date Valid
2020-08-29
Language
English
Type
Form
electronic documents
Department name
Mathematics
Digital Format
electronic documents
Media type
Creator role
Graduate Student
Identifier
1131779495
https://asa.lib.lehigh.edu/Record/11134142
Subject (LCSH)
Dyson, . A. (2019). Existence, Uniqueness, and Stability of Traveling Waves in Neural Field Models (1–). https://preserve.lehigh.edu/lehigh-scholarship/graduate-publications-theses-dissertations/theses-dissertations/existence
Dyson, Alan. 2019. “Existence, Uniqueness, and Stability of Traveling Waves in Neural Field Models”. https://preserve.lehigh.edu/lehigh-scholarship/graduate-publications-theses-dissertations/theses-dissertations/existence.
Dyson, Alan. Existence, Uniqueness, and Stability of Traveling Waves in Neural Field Models. Jan. 2019, https://preserve.lehigh.edu/lehigh-scholarship/graduate-publications-theses-dissertations/theses-dissertations/existence.