Random currents through nerve membranes. I. Uniform Poisson or white noise current in one-dimensional cables
The linear cable equation with uniform Poisson or white noise input is studied. The solutions of these stochastic equations are derived from Green's function representation of the solution of a corresponding deterministic cable equation. The mean, variance and covariance are computed for various cable length and boundary conditions. The spectral density is examined in the fixed point of the cable to infinite as well as finite cable. The first passage time problem is solved for the diffusion model. Numerical ad simulation techniques are employed to illustrate the derived results. The authors propose the theory as a model for the voltage across the membrane of a one- dimensional nerve cylinder.
voltage across the membrane of a one-dimensional nerve cylinder
scientific article; zbMATH DE number 3852858