Harris, Jeremy D
(2017)
Analysis of a Spatially-distributed Wilson-Cowan Model of Cortex.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
The Wilson-Cowan equations represent a model for the mean activities of localized excitatory and inhibitory populations in sensory cortex. In this document, we extend this model to include spatially-distributed connections in a 1D continuum model to study spatiotemporal patterns, such as traveling waves and doubly periodic patterns. We use bifurcation theory and continuation methods to understand how these organized patterns of activity arise in the network. In addition, we often simulate a (spatial) discretization of the network (to approximate the continuum) and compare these with our analytical theory to give evidence as to how these patterns may become unstable. In the later chapters, we make comparisons with a nonsmooth version of the model to understand the consequences of this approximation.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
25 June 2017 |
| Date Type: |
Publication |
| Defense Date: |
13 April 2017 |
| Approval Date: |
25 June 2017 |
| Submission Date: |
14 April 2017 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
133 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Neural field model; dynamical systems; spatiotemporal patterns; traveling waves; |
| Date Deposited: |
25 Jun 2017 21:37 |
| Last Modified: |
25 Jun 2017 21:37 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/31323 |
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