期刊
JOURNAL OF DIFFERENTIAL EQUATIONS
卷 174, 期 2, 页码 312-368出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jdeq.2000.3929
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we give a geometric analysis of relaxation oscillations and canard cycles in singularly perturbed planar vector fields. The transition from small Hopf-type cycles to large relaxation cycles, which occurs in an exponentially thin parameter interval, is described as a perturbation of a family of singular cycles. The results are obtained by means of two blow-up transformations combined with standard tools of dynamical systems theory. The efficient use of various charts is emphasized. The results are applied to the van der Pol equation. (C) 2001 Academic Press.
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