  We study the noise activated dynamics of a model {\it autapse} neuron system
that consists of a subcritical Hopf oscillator with a time delayed nonlinear
feedback. The coherence of the noise driven pulses of the neuron exhibits a
novel double peaked structure as a function of the noise amplitude. The two
peaks correspond to separate optimal noise levels for excitation of single
spikes and multiple spikes (bursts) respectively. The relative magnitudes of
these peaks are found to be a sensitive function of time delay. The physical
significance of our results and its practical implications in various real life
systems are discussed.
