Wilson-Cowan Neural Mass

The Wilson-Cowan model describes interacting populations of excitatory (E) and inhibitory (I) neurons. The equations are:
τ_E Ė = −E + S(w_EE·E − w_EI·I + P_E)  |  τ_I İ = −I + S(w_IE·E − w_II·I + P_I)
where S(x) = 1/(1+e^{−x}) is the sigmoid gain function. Depending on coupling weights, the system exhibits stable fixed points, limit cycle oscillations (gamma/beta rhythms), or bistability. Left: time series of E (magenta) and I (cyan). Right: phase portrait with nullclines.