We study the noise activated dynamics of a model 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.
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