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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.
Mathematics Subject Classification: Primary: 37B55; 34K14; Secondary: 92C20.

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