We undertake a probabilistic analysis of the response of
repetitively firing neural populations to simple pulselike
stimuli. This work is motivated by experimental data which shows
that neurons in a region of the brain known as the locus coeruleus
(LC) can exhibit distinct firing patterns which are strongly
correlated with performance on cognitive tasks. Using a phase
oscillator model for the LC neurons, we compute average firing
probabilities for a pool of neurons in response to stimuli over
many trials. This involves the solution of an advection-diffusion
equation, and shows that neural response (1) is elevated in
populations with lower baseline firing rates, and (2) decays due
to noise and distributions of neuron frequencies. Similar results
are obtained for other types of neurons, although the details of
the response depend crucially on the type of bifurcation which
leads to their repetitive firing.
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