L. S. Borkowski, PHYSICAL REVIEW E 80, 051914 (2009)

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 Ti. For T_i>T* even multiples of Ti 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.

DOI: 10.1103/PhysRevE.80.051914