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Based on the boundary layer function method, a class of generalized high-dimensional delayed systems in the critical case is studied. In the framework of this paper, we not only construct the asymptotic expansion of the solution for the original equation but also give the proof of the uniformly valid asymptotic expansion. Meanwhile, we give an example to demonstrate our result.doi:10.1186/s13662-015-0502-y fatcat:oopphjjvwvefhmqm6glby3yebm