Palkar, Grishma
(2021)
UNDERSTANDING THE EFFECT OF INHIBITION ON THE TRAVELING WAVES IN A NEURONAL NETWORK.
Master's Thesis, University of Pittsburgh.
(Unpublished)
Abstract
We study the effect of inhibition on the traveling waves arising in the neuronal networks. A neuronal firing rate model of the sensory cortex has two population types, excitatory and inhibitory. We are interested in the case when we have three fixed points: (1) a stable downstate; (2) a saddle point with a stable manifold that acts as a threshold for firing; (3) an upstate. We will look at the case when the upstate is unstable, which gives rise to pulse (a transient increase in firing that returns to the downstate). We will first study the effects of inhibition on the spiking neuronal model. Then we will reduce the spiking neuronal model to a Wilson-Cowan like equations and try to mimic the results that we obtained in the original spiking model. In the Wilson-Cowan equations, we first look at the model with smooth firing rate function and later with Heaviside firing rate function. In the Heaviside firing rate case, we investigate the existence of the traveling wave and study the stability using the Evans-function (a complex analytic function obtained by linearizing a system about its traveling wave and whose zeros give the eigenvalues of the linearized operator). The Evans function allows us to study the stability of a given wave and identify bifurcation points (loss of stability) as the spatial extent of inhibition is varied. We observe an Andronov-Hopf bifurcation and later we explore the behavior of the traveling waves as the spatial scales of the inhibition population change and notice oscillatory instability.
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Details
| Item Type: |
University of Pittsburgh ETD
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| Status: |
Unpublished |
| Creators/Authors: |
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| ETD Committee: |
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| Date: |
20 January 2021 |
| Date Type: |
Publication |
| Defense Date: |
24 November 2020 |
| Approval Date: |
20 January 2021 |
| Submission Date: |
4 December 2020 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
46 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Mathematics |
| Degree: |
MS - Master of Science |
| Thesis Type: |
Master's Thesis |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
Neuronal Network
Wilson-Cowan equations
inhibition |
| Date Deposited: |
20 Jan 2021 19:36 |
| Last Modified: |
20 Jan 2021 19:36 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/39984 |
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