Effects of synaptic depression and adaptation on spatiotemporal dynamics of an excitatory neuronal network

By Zachary P. Kilpatrick, Paul C. Bressloff. 2010

112 citations recorded by the source corpus.

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.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/036f0d879ae404e49b504b43ff94a4b7c0af00e0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Cognitive Neuroscience

1. Paul C. Bressloff
2. Stephen Coombes
3. Brent Doiron
4. Robert Rosenbaum

In Computer Networks and Communications

1. Paul C. Bressloff
2. Robert Rosenbaum
3. Brent Doiron

In Statistical and Nonlinear Physics

1. Paul C. Bressloff
2. Brent Doiron
3. Robert Rosenbaum
4. Karl J. Friston

Citations in the corpus

• Spatiotemporal dynamics of continuum neural fields (2012, background): “Other extensions include weight distributions that are not of the lateral inhibition type (for which multiple bump states can arise) [28, 88], spiking rather than rate-based models [139, 140], weakly interacting bumps [105], and bumps in adaptive neural fields [61, 64, 141].”