Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 387, Issue 7, Pages 1455-1463Publisher
ELSEVIER
DOI: 10.1016/j.physa.2007.10.062
Keywords
nonlinear diffusion; stochastic partial differential equations; neurons
Categories
Ask authors/readers for more resources
We consider a general nonlinear diffusion, typified by those deriving from Fitzhugh-Nagumo or Hindmarsh-Rose models of nerve-cell dynamics, perturbed also by 2-parameter white noise. In order to investigate the effects of the nonlinearity, we find for general boundary conditions the mean to order is an element of(2) and the four-point covariance to order is an element of(3). The derivations involve multiple stochastic integrals in the plane. The mean and variance of the state variable are thus obtained and may be used to estimate the probabilities that a threshold value is exceeded as a function of space and time. A numerical example is given for a space-time white-noise driven diffusion with a cubic nonlinearity. From the asymptotic form of the covariance the spectral density of the process can also be obtained. (c) 2007 Elsevier B.V. All rights reserved.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available