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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homoclinic loop and multiple limit cycle bifurcation surfaces


Author: L. M. Perko
Journal: Trans. Amer. Math. Soc. 344 (1994), 101-130
MSC: Primary 58F14; Secondary 34C23, 34C37, 58F21
MathSciNet review: 1227092
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Abstract: This paper establishes the existence and analyticity of homoclinic loop bifurcation surfaces $ \mathcal{H}$ and multiplicity-two, limit cycle bifurcation surfaces $ \mathcal{C}$ for planar systems depending on two or more parameters; it determines the side of $ \mathcal{H}$ or $ \mathcal{C}$ on which limit cycles occur; and it shows that if $ \mathcal{H}$ and $ \mathcal{C}$ intersect, then typically they do so at a flat contact.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1994-1227092-6
PII: S 0002-9947(1994)1227092-6
Article copyright: © Copyright 1994 American Mathematical Society