Singularly perturbed Cauchy problems and contrast structures (Q1811510)

The authors consider the Cauchy problem for a singularly perturbed system of second-order differential equations. Sufficient conditions for the appearance of contrast structures of step and spike types for systems with piecewise smooth right-hand side were obtained by the authors [Differ. Equ. 36, No. 11, 1493--1510 (2000; Zbl 1056.34520), ibid. 37, No. 11, 1580--1588 (2001; Zbl 1034.34067)]. In the present paper, the authors describe these conditions more specifically for general two-dimensional singularly perturbed Cauchy problems with smooth right-hand sides in the form of constraints imposed on the right-hand side. Furthermore, they estimate the step time and magnitude. Several examples are given.