On the Limit Cycles of a Class of Planar Singular Perturbed Differential Equations. (30th March 2014)

• Record Type: Journal Article
• Authors: Wu, Yuhai; Zhou, Jingjing
• Other Names: Han M. Academic Editor.; Jin Z. Academic Editor.; Xia Y. Academic Editor.
• Is Part Of: TheScientificWorldjournal. Volume 2014(2014)
• Publication Date: 2014-03-30
• Subjects: Science -- Periodicals; Technology -- Periodicals; Medicine -- Periodicals; 505
• DOI: 10.1155/2014/379897
• Languages: English
• ISSNs: 2356-6140

Abstract

Abstract : 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.