Wilson-Cowan neural field on a ring models cortical working memory.
The activity field u(x,t) evolves via:
τ ∂u/∂t = −u + ∫ w(x−x′) f[u(x′)] dx′ + I(x)
The kernel w(x) = A exp(−x²/2σ²_E) − B exp(−x²/2σ²_I) (Mexican hat)
supports a stable
bump of activity that can sit at any location on the ring —
a
continuous attractor encoding a remembered angle (head direction, working memory).
Click the canvas to inject input at a location.