Boundary Value Problems
Volume 2009 (2009), Article ID 634324, 17 pages
doi:10.1155/2009/634324

On step-like contrast structure of singularly perturbed systems

Abstract

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.