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Open Access Research Article

On Step-Like Contrast Structure of Singularly Perturbed Systems

Mingkang Ni and Zhiming Wang*

Author Affiliations

Department of Mathematics, East China Normal University, Shanghai 200241, China

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Boundary Value Problems 2009, 2009:634324  doi:10.1155/2009/634324

Published: 23 August 2009

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.