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Transactions of the American Mathematical Society

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Separatrix and limit cycles of quadratic systems and Dulac's theorem


Authors: Carmen Chicone and Douglas S. Shafer
Journal: Trans. Amer. Math. Soc. 278 (1983), 585-612
MSC: Primary 58F21; Secondary 34C05
DOI: https://doi.org/10.1090/S0002-9947-1983-0701513-X
MathSciNet review: 701513
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Abstract: Separatrix cycles for a planar quadratic vector field are studied. The results obtained are used to show that in any bounded region of the plane a quadratic vector field has at most a finite number of limit cycles.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0701513-X
Keywords: Limit cycle, quadratic system, separatrix cycle, Dulac's Theorem
Article copyright: © Copyright 1983 American Mathematical Society