Random currents through nerve membranes. I. Uniform Poisson or white noise current in one-dimensional cables. (English) Zbl 0536.92019
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.
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.
Reviewer: P.Lánský
MSC:
| 92Cxx | Physiological, cellular and medical topics |
| 60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
| 65C20 | Probabilistic models, generic numerical methods in probability and statistics |
Keywords:
random currents; nerve membranes; Fourier series representation; linear cable equation; uniform Poisson or white noise input; Green’s function representation; mean; variance; covariance; spectral density; first passage time problem; diffusion model; voltage across the membrane of a one-dimensional nerve cylinderReferences:
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