Spirals and auto-soliton scattering: interface analysis in a neural field model  

Project description

Neural field models describe the coarse grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in 2D, where they are well known to generate rich patterns of spatio-temporal activity. Typical patterns include localised solutions in the form of travelling spots as well as spiral waves [1]. These patterns are naturally defined by the interface between low and high states of neural activity. This project will derive the dimensionally reduced equations of motion for such interfaces from the full nonlinear integro-differential equation defining the neural field.  Numerical codes for the evolution of the interface will be developed, and embedded in a continuation framework for performing a systematic bifurcation analysis.  Weakly nonlinear theory will be developed to understand the scattering of multiple spots that behave as auto-solitons, whilst strong scattering solutions will be investigated using the scattor theory that has previously been developed for multi-component reaction diffusion systems [2].