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

TL;DR

This paper investigates how a Hodgkin-Huxley neuron responds to high-frequency periodic stimuli, revealing complex behaviors including mode-locking, chaos, and a sharp transition in interspike interval histograms near a critical period.

Contribution

It provides new insights into the nonlinear and chaotic responses of Hodgkin-Huxley neurons to high-frequency inputs, highlighting a critical transition in firing patterns.

Findings

Response transitions from firing to silence with increasing synaptic conductance.

Interspike interval histogram exhibits a sharp transition at a critical period T*.

Chaotic regimes show sublinear increase in firing rate near the excitation threshold.

Abstract

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.