Different dynamics of repetitive neural spiking induced by inhibitory and excitatory autapses near subcritical Hopf bifurcation

Based on the post-inhibitory rebound (PIR) spike induced by inhibitory current pulse, in the present paper, a novel counterintuitive phenomenon that the inhibitory autapse with time delay can induce the resting state changed to stable spiking pattern is identified near subcritical Hopf bifurcation of Hodgkin-Huxley model. The delayed inhibitory autaptic current pulse induced by the preceded action potential can induce the preceding PIR spike via the hyperpolarization, rebound, and depolarization processes, which is compared with spiking induced by excitatory autapse via only a depolarization process. The threshold of inhibitory or excitatory autaptic conductance to induce spiking with increasing time delay, and the threshold curve of inhibitory or excitatory pulse current to evoke a spike exhibit damping oscillations can be well interpreted with the damping dynamics of focus near subcritical Hopf bifurcation. However, due to PIR mechanism, the threshold conductance of inhibitory autapse is stronger than that of excitatory autapse, and the spiking period for inhibitory autapse, which is composed of time delay and durations of the other three processes, is longer than the one for excitatory autapse, which is composed of time delay and duration of only a depolarization process. Therefore, a linear correlation between spiking period and time delay is identified, which shows that autapse can modulate the spike timing related to temporal coding. The results present a novel viewpoint and a potential function that inhibitory autapse can facilitate spiking like the excitatory autapse and provide effective measures to modulate neuronal spiking pattern, which is related to subcritical Hopf bifurcation.