Abstract
A nonautonomous difference equation is aymptotically autonomous if its right-hand side becomes more and more like that of an autonomous difference equation as time increases. It can then be shown that the component sets of a pullback attractor of the nonautonomous converge to the attractor of the autonomous system. Various conditions ensuring this both in the Hausdorff semi-metric and the full Hausdorff metric are given. Asymptotic equivalence of nonautonomous difference equations is also considered in the backwards sense. Both single-valued and set-valued difference equations are investigated. The results are applied to a simplified example of a discrete time neural field lattice model with both single-valued and set-valued interaction terms.
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