Math Biology Seminar: Cindy Greenwood

A diffusion-type operator biologically significant in neuroscience is a difference of Gaussian functions used as a spatial-convolution kernel (Mexican-Hat operator). We are interested in the dynamics inherent in a neural structure such as visual cortex modeled by stochastic neural field equations, a class of stochastic differential-integral equations using the Mexican-Hat kernel. We find that spatially smoothed noise, in a field of Ornstein-Uhlenbeck processes, without direct spatial coupling, causes pattern formation. Our analysis of the interaction between coupling and noise-sharing yields optimal parameter combinations for the formation of spatial pattern. Joint work with PH Baxendale and LM Ward, recently on line, Phys.Rev.E