  In this work we consider the nonlocal evolution equation $$ \frac{\partial
u(w,t)}{\partial t}=-u(w,t)+ \int_{S^{1}}J(wz^{-1})f(u(z,t))dz+ h, \,\,\, h > 0
$$ which arises in models of neuronal activity, in $L^{2}(S^{1})$, where
$S^{1}$ denotes the unit sphere. We obtain stronger results on existence of
global attractors and Lypaunov functional than the already existing in the
literature. Furthermore, we prove the result, not yet known in the literature,
of lower semicontinuity of global attractors with respect to connectivity
function $J$.
