Localized activity bumps in spatially extended neural populations
The Amari (1977) neural field model describes the evolution of population firing rate u(x,t) via τ∂ₜu = −u + ∫w(x−x')f(u(x'))dx' + I(x). The Mexican-hat connectivity kernel w = A_e·exp(−x²/2σ_e²) − A_i·exp(−x²/2σ_i²) supports stable localized "bump" attractors encoding working memory locations. Click the canvas to inject a stimulus and form bumps.