Neural Field Theory — Wilson-Cowan Waves

Wilson-Cowan (1972): τ_E dE/dt = −E + S(w_ee·(K*E) − w_ie·(K*I) + I_ext), τ_I dI/dt = −I + S(w_ei·(K*E) − w_ii·I). Sigmoidal gain S(x) = 1/(1+e^{−x}). Spatial kernel K(x)=exp(−|x|/σ). Rich dynamics: homogeneous steady states, Turing instability → spatial patterns, oscillations, traveling waves. Models: EEG rhythms, cortical spreading depression, working memory bumps.