Wilson–Cowan continuum model — localised activity and propagating fronts
The neural field equation: τ ∂u/∂t = −u + ∫w(x−x')f(u(x'))dx' + I(x), where w is a Mexican-hat kernel (excitatory-inhibitory) and f(u)=1/(1+e^{−(u−θ)/0.1}) is a sigmoid firing rate. Depending on parameters, the field supports stationary bumps (working memory), oscillations, and travelling waves. This model underlies theories of visual hallucinations (Bressloff 2001) and cortical propagation.