Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network
File(s)
Accepted version
Author(s)
Kilpatrick, Zachary P
Bressloff, Paul C
Type
Journal Article
Abstract
We analyze the spatiotemporal dynamics of a system of integro-differential equations that describes a one-dimensional excitatory neuronal network with synaptic depression and spike frequency adaptation. Physiologically suggestive forms are used for both types of negative feedback. We also consider the effects of employing two different types of firing rate function, a Heaviside step function and a piecewise linear function. We first derive conditions for the existence of traveling fronts and pulses in the case of a Heaviside step firing rate, and show that adaptation plays a relatively minor role in determining the characteristics of traveling waves. We then derive conditions for the existence and stability of stationary pulses or bumps, and show that a purely excitatory network with synaptic depression cannot support stable bumps. However, bumps do not exist in the presence of adaptation. Finally, in the case of a piecewise linear firing rate function, we show numerically that the network also supports self-sustained oscillations between an Up state and a Down state, in which a spatially localized oscillating core periodically emits pulses at each cycle.
Date Issued
2010-05-01
Date Acceptance
2009-06-01
Citation
Physica D: Nonlinear Phenomena, 2010, 239 (9), pp.547-560
ISSN
0167-2789
Publisher
Elsevier BV
Start Page
547
End Page
560
Journal / Book Title
Physica D: Nonlinear Phenomena
Volume
239
Issue
9
Copyright Statement
Copyright © Elsevier Ltd. All rights reserved. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https://creativecommons.org/licenses/by-nc-nd/4.0/
Identifier
http://dx.doi.org/10.1016/j.physd.2009.06.003
Publication Status
Published
Date Publish Online
2009-06-13