Homoclinic loop and multiple limit cycle bifurcation surfaces
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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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 344 (1994), 101-130
- MSC: Primary 58F14; Secondary 34C23, 34C37, 58F21
- DOI: https://doi.org/10.1090/S0002-9947-1994-1227092-6
- MathSciNet review: 1227092