Two coupled neural populations (excitatory E, inhibitory I) on a 1D cortical sheet. Spatial coupling via Mexican-hat kernels produces traveling waves, bumps, and oscillations.
dE/dt = -E + S(wEE*[K*E] - wIE*I + Iext + noise). dI/dt = -I + S(wEI*[K*E] - wII*I). Sigmoid S(x)=1/(1+e^{-x}). Kernel K(x)=exp(-x²/2σ²). Green=excitatory, red=inhibitory.