Abstract:

The step-type contrast structure for a singularly perturbed system with slow and fast variables is considered. We not only construct the heteroclinic orbit by first integral, but also determine the internal transition time t. The asymptotic expansion of this problem with a step-type contrast structure is constructed by the boundary function method. By sewing orbit smooth, the existence of the step-type contrast structure is shown and the asymptotic solution is proved to be uniformly in the whole interval.

Key words: singulary perturbed; step-type contrast structure; boundary function; first integral