| Summary: | In this work we study the pullback dynamics of a class of nonlocal non-autonomous evolution equations for neural fields in a bounded smooth domain $\Omega$ in $\mathbb{R}^N$
\[
\begin{cases}
\partial_t u(t,x) =- u(t,x) + \displaystyle\int_{\mathbb{R}^N} J(x,y)f(t,u(t,y))dy,\ t\geq\tau,\ x \in \Omega,\\
u(\tau,x)=u_\tau(x),\ x\in\Omega,
\end{cases}
\]
with $u(t,x)= 0,\ t\geq\tau,\ x \in\mathbb{R}^N\backslash\Omega$, where the integrable function $J: \mathbb{R}^N \times \mathbb{R}^{N}\to \mathbb{R}$ is continuously differentiable, $\int_{\mathbb{R}^N} J(x,y) dy = \int_{\mathbb{R}^N} J(x,y) dx= 1$ and symmetric i.e., $J(x,y)=J(y,x)$ for any $x,y \in \mathbb{R}^N$. Under suitable assumptions on the nonlinearity $f: \mathbb{R}^2\to\mathbb{R}$, we prove existence, regularity and upper semicontinuity of pullback attractors for the evolution process associated to this problem.
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