Existence and upper semicontinuity of global attractors for neural fields in an unbounded domain

Abstract

In this article, we prove the existence and upper semicontinuity of compact global attractors for the flow of the equation $$ frac{partial u(x,t)}{partial t}=-u(x,t)+ J*(fcirc u)(x,t)+ h, quad h > 0, $$ in $L^{2}$ weighted spaces.

Keywords

• Well-posedness
• global attractor
• upper semicontinuity of attractors