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Response of a Hodgkin-Huxley neuron to a high-frequency input

We study the response of a Hodgkin-Huxley neuron stimulated by a periodic sequence of conductance pulses arriving through the synapse in the high frequency regime. In addition to the usual excitation threshold there is a smooth crossover from the firing to the silent regime for increasing pulse amplitude $g_{syn}$. The amplitude of the voltage spikes decreases approximately linearly with $g_{syn}$. In some regions of parameter space the response is irregular, probably chaotic. In the chaotic regime between the mode-locked regions 3:1 and 2:1 near the lower excitation threshold the output interspike interval histogram (ISIH) undergoes a sharp transition. If the driving period is below the critical value, $T_i < T^*$, the output histogram contains only odd multiples of $T_i$. For $T_i > T^*$ even multiples of $T_i$ also appear in the histogram, starting from the largest values. Near $T^*$ the ISIH scales logarithmically on both sides of the transition. The coefficient of variation of ISIH has a cusp singularity at $T^*$. The average response period has a maximum slightly above $T^*$. Near the excitation threshold in the chaotic regime the average firing rate rises sublinearly from frequencies of order 1 Hz.