Copyright © 2009 Mingkang Ni and Zhiming Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The existence of a
step-like contrast structure for a class of
high-dimensional singularly perturbed system is
shown by a smooth connection method based on the
existence of a first integral for an associated
system. In the framework of this paper, we not
only give the conditions under which there
exists an internal transition layer but also
determine where an internal transition time is.
Meanwhile, the uniformly valid asymptotic
expansion of a solution with a step-like
contrast structure is presented.