Dissertation
Traveling front solution stability in a lateral inhibition network in the neural field model
Doctor of Philosophy (Ph.D.), Drexel University
Jun 2022
DOI:
https://doi.org/10.17918/00001185
Abstract
In this paper, we derive the stability for Traveling Front Solutions of the Neural Field Model first presented by Amari. We proceed by using the method of linearization and finding equivalent ODE's for our eigenvalue integrodifferential equation using a differentiation approach. We then convert the ODE's for above and below threshold solutions into systems of first order ODE's in order to find the eigenvalues and eigenvectors of our equations. Finally, we compute the Evan's function for our systems and use a numerical analysis approach to determine the stability of the traveling front solutions. We do this in three settings for the stability eigenvalues, one for [gamma] [is an element of] R, one for [gamma] [is an element of] C with complex-valued Evans function, and one for [gamma] [is an element of] C with a real-valued Evans function that is an equivalent system to the complex-valued Evans function.
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Details
- Title
- Traveling front solution stability in a lateral inhibition network in the neural field model
- Creators
- Dominick John Macaluso
- Contributors
- Yixin Guo (Advisor)
- Awarding Institution
- Drexel University
- Degree Awarded
- Doctor of Philosophy (Ph.D.)
- Publisher
- Drexel University; Philadelphia, Pennsylvania
- Number of pages
- ix, 121 pages
- Resource Type
- Dissertation
- Language
- English
- Academic Unit
- College of Arts and Sciences; Drexel University; Mathematics
- Other Identifier
- 991018527108104721