The interfacial dynamics of Amari type neural field models on finite domains - Gokce, Aytul (2017)
Continuum neural field models mimic the large scale spatio-temporal dynamics of interacting neurons on a cortical surface. For smooth Mexican hat kernels, with short-range excitation and long-range inhibition, they support various localised structures as well as travelling waves similar to those seen in real cortex. These non-local models have been extensively studied, both analytically and numerically, yet there remain open challenges in their study. Here we provide new numerical and analytical treatments for the study of spatio-temporal pattern formation in neural field models. In this context, the description of spreading patterns with a well identified interface is of particular interest, as is their dependence on boundary conditions.