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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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