| 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 |
| ID |
192810 |
| Reference URL |
https://collections.lib.utah.edu/ark:/87278/s65x2qg3 |
