Open Collections

Pattern formation via stochastic neural field equations

Banff International Research Station for Mathematical Innovation and Discovery

The formation of pattern in biological systems may be modeled by a set of reaction-diffusion equations. A form of diffusion-type coupling term biologically significant in neuroscience is a difference of Gaussian functions used as a space-convolution kernel. Here we study the simplest reaction-diffusion system with this type of coupling. Instead of the deterministic form of the model, we are interested in a \emph{stochastic} neural field equation, a space-time stochastic differential-integral equation. We explore, quantitatively, how the parameters of our model that measure the shape of the coupling kernel, coupling strength, and aspects of the spatially-smoothed space-time noise, control the pattern in the resulting evolving random field. We find that a spatial pattern that is damped in time in a deterministic system may be sustained and amplified by stochasticity, most strikingly at an optimal space-time noise level.

Mathematics; Statistics; Probability theory and stochastic processes; Applied statistics

video/mp4

Author affiliation: University of British Columbia

2017-08-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/62837

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/