TY - JOUR AU - Ni, Mingkang AU - Wang, Zhiming PY - 2009 DA - 2009/08/23 TI - On Step-Like Contrast Structure of Singularly Perturbed Systems JO - Boundary Value Problems SP - 634324 VL - 2009 IS - 1 AB - 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. SN - 1687-2770 UR - https://doi.org/10.1155/2009/634324 DO - 10.1155/2009/634324 ID - Ni2009 ER -