Localized persistent activity as a neural model of working memory
A continuum model of cortex: neural field u(x,t) evolves under lateral inhibitory interactions. Stable bumps of activity emerge and persist — a model of spatial working memory.
The Mexican-hat connectivity kernel w(x) (local excitation, lateral inhibition) supports bumps:
The bump's existence and stability depend on the kernel parameters. The bump position encodes a memorized location — a continuous attractor.
Multiple bumps can coexist if inhibition is sufficiently local.