  We analyze the stability of standing pulse solutions of a neural network
integro-differential equation. The network consists of a coarse-grained layer
of neurons synaptically connected by lateral inhibition with a non-saturating
nonlinear gain function. When two standing single-pulse solutions coexist, the
small pulse is unstable, and the large pulse is stable. The large single-pulse
is bistable with the ``all-off'' state. This bistable localized activity may
have strong implications for the mechanism underlying working memory. We show
that dimple pulses have similar stability properties to large pulses but double
pulses are unstable.
