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The Scientific World Journal
Volume 2014, Article ID 379897, 10 pages
Research Article

On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations

Department of Mathematics, Jiangsu University, Zhenjiang 212013, China

Received 7 December 2013; Accepted 10 February 2014; Published 31 March 2014

Academic Editors: M. Han, Z. Jin, and Y. Xia

Copyright © 2014 Yuhai Wu and Jingjing Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Relaxation oscillations of two-dimensional planar singular perturbed systems with a layer equation exhibiting canard cycles are studied. The canard cycles under consideration contain two turning points and two jump points. We suppose that there exist three parameters permitting generic breaking at both the turning points and the connecting fast orbit. The conditions of one (resp., two, three) relaxation oscillation near the canard cycles are given by studying a map from the space of phase parameters to the space of breaking parameters.