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.