Stochastic incoherence in the response of rebound bursters

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.