Voltage-noise-induced transitions in electrically excitable membranes

A quantitative study of the steady-state behavior of the sodium and potassium conductance for the Hodgkin-Huxley axon under the influence of an externally driven voltage noise is reported. The dichotomous Markov noise (random telegraph signal) considered allows for an exact evaluation of the stationary probability density of the conductances. Phase diagrams are constructed to represent the response of the system as a function of the amplitude and the correlation time of the noise. The results obtained for the Hodgkin-Huxley axon are compared with some molecular models used in the literature.