Wilson-Cowan Neural Mass Model

The Wilson-Cowan equations describe mean activity of coupled excitatory (E) and inhibitory (I) neural populations. τ dE/dt = -E + S(w_EE·E - w_EI·I + P) and τ dI/dt = -I + S(w_IE·E - w_II·I). Depending on coupling, the system shows fixed points, limit cycles (neural oscillations), or bistability.

Parameters

Excit→Excit w_EE: 16 Excit→Inhib w_IE: 15 Inhib→Excit w_EI: 12 External input P: 1.25 Time const τ: 8 ms

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S(x) = 1/(1+exp(-x+θ)). E=excitatory, I=inhibitory population rates. Phase plane shows nullclines and trajectory. Hopf bifurcation creates limit cycle oscillations at ~40Hz gamma rhythms.