Neural Field Theory — Wilson-Cowan Spatial

Excitatory-inhibitory waves · Turing instability in cortex · bump attractors

Connectivity Parameters

Wilson-Cowan (1972): τ_E dE/dt = −E + S(w_EE⊛E − w_EI⊛I + h_E)

Mexican-hat connectivity: Short-range excitation, long-range inhibition → Turing instability → cortical waves and "bump attractors" (working memory).

Phenomena: Traveling waves (γ-band ~40Hz), standing waves, spatially localized bumps (as in visual hallucinations, migraine aura).

Red = excitatory activity; Blue = inhibitory. Patterns self-organize from noise.