The Amari neural field equation ∂u/∂t = −u + ∫w(x−x')f(u(x'))dx' + I(x) with Mexican-hat connectivity w produces localized activity bumps — a model for spatial working memory.
Excitation width σ_e15
Inhibition width σ_i35
Inhibition strength A_i0.50
Input strength10
Click the canvas to place a localized input. The bump is stable and can be moved by external input — spatial working memory. With strong inhibition, the bump suppresses activity elsewhere. The Mexican-hat kernel w(x) = A_e·exp(−x²/2σ_e²) − A_i·exp(−x²/2σ_i²) shown below.