Bifurcation of limit cycles: geometric theory
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 by L. M. Perko PDF
 Proc. Amer. Math. Soc. 114 (1992), 225236 Request permission
Abstract:
Multiple limit cycles play a basic role in the theory of bifurcations. In this paper we distinguish between singular and nonsingular, multiple limit cycles of a system defined by a oneparameter family of planar vector fields. It is shown that the only possible bifurcation at a nonsingular, multiple limit cycle is a saddlenode bifurcation and that locally the resulting stable and unstable limit cycles expand and contract monotonically as the parameter varies in a certain sense. Furthermore, this same type of geometrical behavior occurs in any oneparameter family of limit cycles experiencing a saddlenode type bifurcation except possibly at a finite number of points on the multiple limit cycle.References

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Additional Information
 © Copyright 1992 American Mathematical Society
 Journal: Proc. Amer. Math. Soc. 114 (1992), 225236
 MSC: Primary 34C23; Secondary 34C05, 34C25
 DOI: https://doi.org/10.1090/S00029939199210863411
 MathSciNet review: 1086341