Large Scale Spatially Organized Activity in Neural Nets

A model for the spatiotemporal activity of neuronal nets is proposed. Stationary periodic spatial patterns are discussed from the point of view of bifurcation theory. Existence of spatial patterns on the whole line is established by the implicit function theorem. Singularity theory is used to study the local structure of the bifurcation equations. A Poincaré–Lindstedt series is developed to establish the form of the periodic stationary states and their stability. The biological relevance of these patterns is briefly discussed.