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Properties of a white-noise driven nonlinear spatially extended model neuron
We derive expressions for the mean, covariance and variance, and their steady state forms, of the voltage in a nonlinear cable driven by a space-time white noise current, under the assumption of sealed end boundary conditions for relatively small disturbances from an equilibrium point. The spectral density of the voltage is also obtained.
Numerical examples are given to highlight the difference between the properties of nonlinear and linear cables. In many cases the differences are small, but often they are substantial. The contributions to the moments from noise are compared with those from the nonlinearity. We fit the spectral density of the voltage in nonlinear cables to Lorentzians and compare their values with those of linear cables and point-model neurons.