Wilson-Cowan Neural Field
Spatially extended excitatory-inhibitory neural population dynamics — traveling waves, spirals, oscillations
Connectivity
E-E coupling w_ee:
12
E-I coupling w_ei:
10
I-E coupling w_ie:
8
I-I coupling w_ii:
3
Dynamics
External input P_e:
0.5
τ_e / τ_i ratio:
0.5
Sigmoid steepness:
1.2
Inject Pulse
Reset
View: E activity
τ_e dE/dt = -E + S(w_ee⊗E - w_ei⊗I + P_e)
τ_i dI/dt = -I + S(w_ie⊗E - w_ii⊗I)
S(x) = 1/(1+e^{-sx})
Wilson-Cowan (1972) equations model interacting populations of excitatory (E) and inhibitory (I) neurons. Spatial coupling enables traveling waves, standing oscillations, and Turing-like pattern formation.