The minimal integrate-and-fire-or-burst (IFB) neuron model reproduces the salient features of
experimentally observed thalamocortical (TC) relay neuron response properties, including the tem-
poral tuning of both tonic spiking (i.e., conventional action potentials) and post-inhibitory rebound
bursting mediated by a low-threshold calcium current. In this paper we consider networks of IFB
neurons with slow synaptic interactions and show how the dynamics may be described with a
smooth firing rate model. When the firing rate of the IFB model is dominated by a refractory
process the equations of motion simplify and may be solved exactly. Numerical simulations are
used to show that a pair of reciprocally interacting inhibitory spiking IFB TC neurons supports
an alternating rhythm of the type predicted from the firing rate theory. A change in a single
parameter of the IFB neuron allows it to fire a burst of spikes in response to a depolarizing signal,
so that it mimics the behavior of a reticular (RE) cell. Within a continuum model we show that
a network of RE cells with on-center excitation can support a fast traveling pulse. In contrast a
network of inhibitory TC cells is found to support a slowly propagating lurching pulse.
This pre-print has been submitted, and accepted, to the journal Physical Review E. The definitive version: COOMBES, S., 2003. Dynamics of synaptically coupled integrate-and-fire-or-burst neurons. Physical Review E, 67(4), art. no. 041910 is available online at http://pre.aps.org/.