  The dynamics of three mutually coupled cortical neurons with time delays in
the coupling are explored numerically and analytically. The neurons are coupled
in a line, with the middle neuron sending a somewhat stronger projection to the
outer neurons than the feedback it receives, to model for instance the relay of
a signal from primary to higher cortical areas. For a given coupling
architecture, the delays introduce correlations in the time series at the
time-scale of the delay. It was found that the middle neuron leads the outer
ones by the delay time, while the outer neurons are synchronized with zero lag
times. Synchronization is found to be highly dependent on the synaptic time
constant, with faster synapses increasing both the degree of synchronization
and the firing rate. Analysis shows that presynaptic input during the
interspike interval stabilizes the synchronous state, even for arbitrarily weak
coupling, and independent of the initial phase. The finding may be of
significance to synchronization of large groups of cells in the cortex that are
spatially distanced from each other.
