Drover, Jonathan
(2005)
The Interplay of Intrinsic Dynamics and Coupling in Spatially Distributed Neuronal Networks.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
Abstract
We explore three coupled networks. Each is an example of a network whose spatially coupled behavior is dratically different than the behavior of the uncoupled system. 1. An evolution equation such that the intrinsic dynamics of the system are those near a degenerate Hopf bifurcation is explored. The coupled system is bistable and solutions such as waves and persistent localized activity are found. 2. A trapping mechanism that causes long interspike intervals in a network of Hodgkin Huxley neurons coupled with excitatory synaptic coupling is unveiled. This trapping mechanism is formed through the interaction of the time scales present intrinsically and the time scale of the synaptic decay. 3. We construct a model to create the spatial patterns reported by subjects in an experiment when their eyes were stimulated electrically. Phase locked oscillators are used to create boundaries representing phosphenes. Asymmetric coupling causes the lines to move, as in the experiment. Stable stationary solutions and waves are found in a reduced model of evolution/ convolution type.
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| 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Unpublished |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: |
4 October 2005 |
| Date Type: |
Completion |
| Defense Date: |
14 June 2005 |
| Approval Date: |
4 October 2005 |
| Submission Date: |
16 August 2005 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| 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: |
convolution; integral equation; localized persistant activity; ordinary differential equations; phosphene; waves |
| Other ID: |
http://etd.library.pitt.edu/ETD/available/etd-08162005-135431/, etd-08162005-135431 |
| Date Deposited: |
10 Nov 2011 19:59 |
| Last Modified: |
15 Nov 2016 13:49 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/9120 |
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