Excitatory–inhibitory population dynamics with phase portrait
The Wilson–Cowan model (1972) describes coupled excitatory (E) and inhibitory (I) neural populations via τ dE/dt = -E + S(wEE·E - wEI·I + P) and τ dI/dt = -I + S(wIE·E + Q), where S(x) = 1/(1+e^{-x}) is the sigmoid. The system exhibits fixed points, limit cycles, and bistability depending on synaptic weights.