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Oscillatory systems with time-delayed pulsatile feedback appear in variousapplied and theoretical research areas, and received a growing interest in thelast years. For such systems, we report a remarkable scenario ofdestabilization of a periodic regular spiking regime. In the bifurcation pointnumerous regimes with non-equal interspike intervals emerge simultaneously. Weshow that this bifurcation is triggered by the steepness of the oscillator'sphase resetting curve and that the number of the emerging, so-called"jittering" regimes grows exponentially with the delay value. Although thisappears as highly degenerate from a dynamical systems viewpoint, the"multi-jitter" bifurcation occurs robustly in a large class of systems. Weobserve it not only in a paradigmatic phase-reduced model, but also in asimulated Hodgkin-Huxley neuron model and in an experiment with an electroniccircuit.

Multistable jittering in oscillators with pulsatile delayed feedback