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Title: Uniqueness of limit cycles bounded by two invariant parabolas (English)
Author: Sáez, Eduardo
Author: Szántó, Iván
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 57
Issue: 5
Year: 2012
Pages: 521-529
Summary lang: English
Category: math
Summary: In this paper we consider a class of cubic polynomial systems with two invariant parabolas and prove in the parameter space the existence of neighborhoods such that in one the system has a unique limit cycle and in the other the system has at most three limit cycles, bounded by the invariant parabolas. (English)
Keyword: stability
Keyword: limit cycles
Keyword: center
Keyword: bifurcation
Keyword: Matlab
MSC: 34C05
MSC: 37C75
MSC: 37N25
MSC: 58F14
MSC: 58F21
MSC: 92B05
MSC: 92D25
idZBL: Zbl 1262.92003
idMR: MR2984617
DOI: 10.1007/s10492-012-0030-y
Date available: 2012-08-19T22:06:53Z
Last updated: 2020-07-02
Stable URL:
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Reference: [8] : MATLAB: The Language of technical computing Using MATLAB (version 7.0).MatWorks Natwick (2004).
Reference: [9] Sáez, E., Szántó, I.: A cubic system with a limit cycle bounded by two invariant parabolas.Differ. Equations Dyn. Syst. 17 (2009), 163-168. Zbl 1207.34038, MR 2550235, 10.1007/s12591-009-0012-z
Reference: [10] Yang, X.: A survey of cubic systems.Ann. Differ. Equations 7 (1991), 323-363. Zbl 0747.34019, MR 1139341


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