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Attractor minimal sets for nonautonomous type-K
competitive and semi-convex delay differential equations with
applications
Skew-product semiflows induced by semi-convex and type-K
competitive almost periodic delay differential equations are
studied. If $M$ is a compact positively invariant subset of the
skew-product semiflow, then continuous separation of the
skew-product semiflow on $M$ holds. Furthermore, if two minimal
subsets $M_{1}$ and $M_{2}$ of the skew-product semiflow
satisfying completely strongly type-K ordering
$M_{1}$«$^C_K M_{2}$, then $M_{1}$ is an attractor. Finally,
these results are applied to a nonautonomous delayed Hopfield-type
neural networks with the diagonal-nonnegative type-K monotone
interconnection matrix and sufficient conditions are obtained for
the existence of global or partial attractors.