Neural Field Theory — Bumps & Traveling Waves

Field Parameters

Excitation σe 5.0 Inhibition σi 10.0 Excit. strength Ae 1.2 Inhib. strength Ai 0.8 Threshold θ 0.2 τ (time const.) 1.0

Diagnostics

Max activity—

Active fraction—

Bump width—

Mode—

Time0

About

The Amari (1977) neural field equation: τ ∂u/∂t = −u + ∫w(x−y)f(u(y))dy, where w is a Mexican-hat connectivity kernel (excitation − inhibition). Stationary "bumps" model working memory. Traveling waves propagate when asymmetry is introduced. Turing instabilities arise when inhibition is too weak. Adjust σe/σi ratio to switch regimes.