Orientation tuning in a ring of pulse-coupled integrate-and-fire (IF) neurons is analyzed
in terms of spontaneous pattern formation. It is shown how the ring bifurcates from a synchronous
state to a non-phase-locked state whose spike trains are characterized by clustered
but irregular fluctuations of the inter-spike intervals (ISIs). The separation of these clusters
in phase space results in a localized peak of activity as measured by the time-averaged firing
rate of the neurons. This generates a sharp orientation tuning curve that can lock to
a slowly rotating, weakly tuned external stimulus. Under certain conditions the peak can
slowly rotate even to a fixed external stimulus. The ring also exhibits hysteresis due to the subcritical nature of the bifurcation to sharp orientation tuning. Such behavior is shown
to be consistent with a corresponding analog version of the IF model in the limit of slow
synpatic interactions. For fast synapses, the deterministic fluctuations of the ISIs associated
with the tuning curve can support a coefficient of variation (CV) of order unity.
This is a pre-print. The definitive version: BRESSLOFF, P.C., BRESSLOFF, N.W. and COWAN, J.D., 2000. Dynamical mechanism for sharp orientation tuning in an integrate-and-fire model of a cortical hypercolumn. Neural Computation, 12(11), pp.2473-2511.