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

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 gsyn. The amplitude of the voltage spikes decreases approximately linearly with gsyn.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, Ti < T * , the output histogram contains only odd multiples of Ti. For Ti > 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.

Multimodal Transition and Excitability of a Neural Oscillator

“…The global bifurcation diagram of the class 3 ML model for β w = −23 mV closely resembles the class 2 HH model [21] at intermediate frequencies. This is consistent with the remarks of Prescott et al [15] that neurons should not be labeled as being strictly type 2 or type 3.…”

“…The f 0 vs. I 0 dependence in the interval between the MMT and the 2:1 state is approximately linear, as in the HH model [21]. The MMT along the T i axis for β w = −23 mV is shown in Fig.…”

“…There are now large bistable regions of the states 3:1 and 2:1. The short stimulation period part of the diagram, for T i < 5 ms, closely resembles the regime of the HH model where the MMT occurs [21,23]. We have analyzed the histogram of interspike intervals (ISI) and found the same dynamic singularity in the ML model.…”

“…The weight of even modes drops sharply in the vicinity of the minimum of the ring rate. The edges of individual modes near the transition scale logarithmically, as in the HH model [21]. All these signatures of the MMT and the topology of the bifurcation diagram in the vicinity of the MMT in the ML model are identical to the HH model.…”

Response of the Hodgkin-Huxley Neuron to a Periodic Sequence of Biphasic Pulses

“…Irregular ring and desynchronization among a group of ANFs is usually attributed to irregular synaptic input and physiological noise [29,30]. It must be kept in mind however that neurons themselves are strongly nonlinear systems and are capable of irregular ring even in the absence of noise [25,26]. O'Gorman et al showed recently [31,32] that a dynamic instability is a plausible explanation of ring irregularities in stimulated ANF.…”