Neural Nets as Spatio-Temporal Pattern Forming Systems

Models of neural nets are developed from a biological point of view. Small networks are analyzed using techniques from dynamical systems. The behavior of spatially and temporally organized neural fields is then discussed from the point of view of pattern formation. Bifurcation methods, analytic solutions and perturbation methods are applied to these models. 1 Introduction The advent of multi-electrode recordings and imaging techniques has enabled neuroscientists to obtain high spatial and temporal resolution of the electrical activity for populations of neurons in the brain. This has led to a resurgence of interest in the biological community in large scale models of neural activity. This in turn has engaged the interest of physicists and mathematicians in the behavior of these systems. There are many levels in which one can model neural activity from detailed models of single ion channels and synapses (Destexhe et al, 1994) up to "black box" models used to understand psychological ph..