  At an optimal value of the noise intensity, the maximum variability in
rebound burst durations is observed and referred to as a response stochastic
incoherence. A general mechanism underlying this phenomenon is given, being
different from those reported so far in excitable systems. It is shown to be
determined by (i) the monotonic reduction of the hysteresis responsible for
bursting caused by noise and consequent transformation of responses from
rebound bursts to single spikes, and (ii) a symmetry breaking in distributions
of burst durations caused by the existence of the minimum response length. The
phenomenon is studied numerically in a Morris-Lecar model for neurons and its
mechanism is explained with the use of canonical models describing hard
excitation states.
