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In this work we consider the nonlocal evolution equation $$ \frac{\partialu(w,t)}{\partial t}=-u(w,t)+ \int_{S^{1}}J(wz^{-1})f(u(z,t))dz+ h, \,\,\, h > 0$$ 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 ofglobal attractors and Lypaunov functional than the already existing in theliterature. Furthermore, we prove the result, not yet known in the literature,of lower semicontinuity of global attractors with respect to connectivityfunction $J$.

Lower semicontinuity of global attractors for a class of evolution equations type neural fields in a bounded domain