Erratum: Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise [Phys. Rev. E83, 051901 (2011)]

Abstract

A very important reference was inadvertently omitted from the list of references in this paper. Paydarfar et al.[1] studied squid giant axons in a bistable regime, where the stable states are in close proximity of each other. They found that noise was capable of annihilating the spiking action. When noise amplitude exceeded a certain threshold, the transition from quiescence to sporadic bursts was induced. The switching between quiescence and sporadic bursts was more frequent for stronger stimuli. They found their experimental results to be qualitatively reproduced in the Hodgkin-Huxley model. The annihilation of repetitive spiking by noise and a transition to sporadic bursts upon an increase of noise level, shown in Fig. 13 of this paper, is an illustration of the same effect.

Multimodal Transition and Excitability of a Neural Oscillator

“…The discrepancy between the type 2 behavior of the HH model and experiment was explained by modifying a single parameter in the term describing the potassium current [18]. In a recent study of the periodically stimulated HH model by the present author it was found that the ring rate may be either continuous or discontinuous function of the current amplitude, depending on the stimulus frequency [19]. Bistable behavior at the excitation threshold appears at non-resonant frequencies [19].…”

“…In a recent study of the periodically stimulated HH model by the present author it was found that the ring rate may be either continuous or discontinuous function of the current amplitude, depending on the stimulus frequency [19]. Bistable behavior at the excitation threshold appears at non-resonant frequencies [19]. When brief stimuli arrive at resonant frequencies, the HH neuron may respond with arbitrarily low ring rate.…”

“…The HH neuron's response at resonant frequencies can be divided into three regimes: (i) short pulses, where the width τ does not exceed the optimal width τ opt associated with a minimum threshold τ opt , (ii) τ opt < τ < T res , and (iii) τ ≈ T res [19]. T res is dened here as the stimulation period for which the amplitude of the membrane potential oscillations is maximum.…”

“…We chose the input current to be a periodic set of rectangular steps of period T i , height I 0 and width τ = 0.5 ms. Studying the HH model, we learned that the topology of the global bifurcation diagram is only weakly dependent on shape details of individual pulses, provided they remain short compared to the time scale of the main resonance [19,26]. The calculations are carried out within the fourth-order RungeKutta scheme with the time step of 0.001 ms.…”

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

“…The type of the near-threshold response depends strongly on stimulation frequency. The ring rate f 0 /f i is a continuous function of the current amplitude near the resonance [27], T i ∼ T res ≈ 17 ms, where T res is the neuron's preferred interspike interval (ISI).…”