Wilson-Cowan Neural Field

Spatially extended excitatory-inhibitory neural population dynamics — traveling waves, spirals, oscillations

Connectivity

Dynamics

τ_e dE/dt = -E + S(w_ee⊗E - w_ei⊗I + P_e)
τ_i dI/dt = -I + S(w_ie⊗E - w_ii⊗I)
S(x) = 1/(1+e^{-sx})
Wilson-Cowan (1972) equations model interacting populations of excitatory (E) and inhibitory (I) neurons. Spatial coupling enables traveling waves, standing oscillations, and Turing-like pattern formation.