Link to the University of Pittsburgh Homepage
Link to the University Library System Homepage Link to the Contact Us Form

The Interplay of Intrinsic Dynamics and Coupling in Spatially Distributed Neuronal Networks

Drover, Jonathan (2005) The Interplay of Intrinsic Dynamics and Coupling in Spatially Distributed Neuronal Networks. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

Primary Text

Download (1MB) | Preview


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.


Social Networking:
Share |


Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Drover, Jonathanjddst25@pitt.eduJDDST25
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairErmentrout, G. Bardbard@pitt.eduBARD
Committee MemberRubin, Jonathanrubin@math.pitt.eduJONRUBIN
Committee MemberUrban,
Committee MemberHastings, Stuartsph@pitt.eduSPH
Committee MemberTroy, W.troy@math.pitt.eduTROY
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:, etd-08162005-135431
Date Deposited: 10 Nov 2011 19:59
Last Modified: 15 Nov 2016 13:49


Monthly Views for the past 3 years

Plum Analytics

Actions (login required)

View Item View Item