

Preprint 15/2008
Analytical and simulation results for the stochastic spatial Fitzhugh-Nagumo model neuron
Henry Tuckwell
Contact the author: Please use for correspondence this email.
Submission date: 10. Feb. 2008
published in: Neural computation, 20 (2008) 12, p. 3003-3033
DOI number (of the published article): 10.1162/neco.2008.08-07-585
Bibtex
Abstract:
For the Fitzhugh-Nagumo system with space-time white noise
we use numerical methods to consider the generation of action potentials
and the reliability of transmission in the presence of noise.
The accuracy of simulated solutions is verified by comparison
with known exact analytical results. Noise of small amplitude
may prevent transmission directly whereas larger amplitude noise
may also interfere by producing secondary non-local responses.
The probability of transmission as a function of noise amplitude is
found for both uniform noise and noise restricted to a patch.
For certain parameter ranges
the recovery variable may be neglected to give a single component
nonlinear diffusion with
space-time white noise. In this case analytical results
are obtained for small perturbations and noise which agree well with
simulation results. For the voltage variable expressions are given for the mean,
covariance and variance, and their
steady state forms.
The spectral density
of the voltage is also obtained.
Numerical examples are given of
the difference between the properties of nonlinear and linear cables and
the validity of the expressions obtained for the statistical properties are
investigated as a function of noise amplitude.
For given parameters, analytical results are in good
agreement with simulation until a certain critical noise amplitude is reached
which can be estimated. The role of trigger zones in increasing the reliability
of transmission is discussed.