Spatially structured waves and oscillations in neuronal networks with synaptic depression and adaptation

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Publication Type dissertation
School or College College of Science
Department Mathematics
Author Kilpatrick, Zachary Peter
Title Spatially structured waves and oscillations in neuronal networks with synaptic depression and adaptation
Date 2010
Description We analyze the spatiotemporal dynamics of systems of nonlocal integro-differential equations, which all represent neuronal networks with synaptic depression and spike frequency adaptation. These networks support a wide range of spatially structured waves, pulses, and oscillations, which are suggestive of phenomena seen in cortical slice experiments and in vivo. In a one-dimensional network with synaptic depression and adaptation, we study traveling waves, standing bumps, and synchronous oscillations. We find that adaptation plays a minor role in determining the speed of waves; the dynamics are dominated by depression. Spatially structured oscillations arise in parameter regimes when the space-clamped version of the network supports limit cycles. Analyzing standing bumps in the network with only depression, we find the stability of bumps is determined by the spectrum of a piecewise smooth operator. We extend these results to a two-dimensional network with only depression.
Type Text
Publisher University of Utah
Subject Integro-differential equations; Neuronal network; Oscillations; Spiral waves; Synaptic depression; Traveling waves
Dissertation Institution University of Utah
Dissertation Name PhD
Language eng
Rights Management ©Zachary Peter Kilpatrick
Format Medium application/pdf
Format Extent 3,585,016 bytes
ARK ark:/87278/s65x2qg3
Setname ir_etd
Date Created 2012-04-23
Date Modified 2021-05-06
ID 192810
Reference URL https://collections.lib.utah.edu/ark:/87278/s65x2qg3