Bistability and resonance in the periodically stimulated Hodgkin-Huxley model with noise

L. S. Borkowski
Phys. Rev. E 83, 051901 – Published 2 May 2011; Erratum Phys. Rev. E 83, 069905 (2011)

Abstract

We describe general characteristics of the Hodgkin-Huxley neuron’s response to a periodic train of short current pulses with Gaussian noise. The deterministic neuron is bistable for antiresonant frequencies. When the stimuli arrive at the resonant frequency the firing rate is a continuous function of the current amplitude I0 and scales as (I0Ith)1/2, characteristic of a saddle-node bifurcation at the threshold Ith. Intervals of continuous irregular response alternate with integer mode-locked regions with bistable excitation edge. There is an even-all multimodal transition between the 2 : 1 and 3 : 1 states in the vicinity of the main resonance, which is analogous to the odd-all transition discovered earlier in the high-frequency regime. For I0<Ith and small noise the firing rate has a maximum at the resonant frequency. For larger noise and subthreshold stimulation the maximum firing rate initially shifts toward lower frequencies, then returns to higher frequencies in the limit of large noise. The stochastic coherence antiresonance, defined as a simultaneous occurrence of (i) the maximum of the coefficient of variation and (ii) the minimum of the firing rate vs the noise intensity, occurs over a wide range of parameter values, including monostable regions. Results of this work can be verified experimentally.

    • Received 14 October 2010

    DOI:https://doi.org/10.1103/PhysRevE.83.051901

    ©2011 American Physical Society

    Erratum

    Authors & Affiliations

    L. S. Borkowski

    • Department of Physics, Adam Mickiewicz University, Umultowska 85, PL-61-614 Poznan, Poland

    Article Text (Subscription Required)

    Click to Expand

    References (Subscription Required)

    Click to Expand
    Issue

    Vol. 83, Iss. 5 — May 2011

    Reuse & Permissions
    Access Options
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required


    ×
    ×

    Images

    ×

    Sign up to receive regular email alerts from Physical Review E

    Log In

    Cancel
    ×

    Search


    Article Lookup

    Paste a citation or DOI

    Enter a citation
    ×