Existence and Uniqueness of Limit Cycles for a Class of Normal Form Equations with Codimension Two Singularities

Existence and Uniqueness of Limit Cycles for a Class of Normal Form Equations with Codimension Two Singularities

In this paper, the existence and uniqueness of limit cycles for a class of normal form equations with codimension two singularities are discussed. By transforming the equations into the generalized Liènard equation, we obtain the sufficient and necessary condition for existence of the unique limit c...

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Veröffentlicht in:Journal of mathematical analysis and applications 1993, Vol.172 (1), p.191-204
Hauptverfasser: Zhang, P.G., Zhao, S.Q.
Format: Artikel
Sprache:eng
Schlagworte:
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Sciences and techniques of general use
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Zusammenfassung:In this paper, the existence and uniqueness of limit cycles for a class of normal form equations with codimension two singularities are discussed. By transforming the equations into the generalized Liènard equation, we obtain the sufficient and necessary condition for existence of the unique limit cycle. And we simplify the proofs on uniqueness of limit cycles. In addition, the parameter conditions on existence of the unique limit cycle are given for a class of equations.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1993.1016