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Analysis of a Spatially-distributed Wilson-Cowan Model of Cortex

Harris, Jeremy D (2017) Analysis of a Spatially-distributed Wilson-Cowan Model of Cortex. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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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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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Harris, Jeremy Djeremy.harris31@gmail.comjdh71
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairErmentrout,
Committee MemberDoiron,
Committee MemberRubin,
Committee MemberUrban,
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


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