  Oscillatory systems with time-delayed pulsatile feedback appear in various
applied and theoretical research areas, and received a growing interest in the
last years. For such systems, we report a remarkable scenario of
destabilization of a periodic regular spiking regime. In the bifurcation point
numerous regimes with non-equal interspike intervals emerge simultaneously. We
show that this bifurcation is triggered by the steepness of the oscillator's
phase resetting curve and that the number of the emerging, so-called
"jittering" regimes grows exponentially with the delay value. Although this
appears as highly degenerate from a dynamical systems viewpoint, the
"multi-jitter" bifurcation occurs robustly in a large class of systems. We
observe it not only in a paradigmatic phase-reduced model, but also in a
simulated Hodgkin-Huxley neuron model and in an experiment with an electronic
circuit.
