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Disconnected

Wilson-Cowan Model

Dynamique de populations excitatrices/inhibitrices

Wilson & Cowan, 1972

Wilson-Cowan Dynamics

Excitatory/Inhibitory populations

Parameters

W_ee10.0
W_ei-4.0
W_ie8.0
W_ii-2.0

State

Excitation (E)0.0000
Inhibition (I)0.0000
Balance (E - |I|)0.0000

Mathematics

Excitatory population:

τEdEdt=−E+S(WEE⋅E+WEI⋅I+Iext)\tau_E \frac{dE}{dt} = -E + S(W_{EE} \cdot E + W_{EI} \cdot I + I_{ext})

Inhibitory population:

τIdIdt=−I+S(WIE⋅E+WII⋅I)\tau_I \frac{dI}{dt} = -I + S(W_{IE} \cdot E + W_{II} \cdot I)

Sigmoid activation:

S(x)=11+e−r(x−θ)S(x) = \frac{1}{1 + e^{-r(x - \theta)}}