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Published in:
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2012 | OriginalPaper | Chapter

7. Limit Cycle Bifurcations Near a Center

Authors : Maoan Han, Pei Yu

Published in: Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles

Publisher: Springer London

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Abstract

In Chap. 7, particular attention is given to bifurcation of limit cycles near a center. After normalizing the Hamiltonian function, detailed steps for computing the Melnikov function are described and formulas are given. Maple programs for computing the coefficients of the Melnikov function are developed and illustrative examples are presented.

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previous chapter Fundamental Theory of the Melnikov Function Method
next chapter Limit Cycles Near a Homoclinic or Heteroclinic Loop
Literature
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Bautin, N.N.: On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type. Mat. Sb. (N. S.) 30(72), 181–196 (1952) MathSciNet
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Hou, Y., Han, M.: Melnikov functions for planar near-Hamiltonian systems and Hopf bifurcations. J. Shanghai Norm. Univ. (Nat. Sci.) 35(1), 1–10 (2006)
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Llibre, J.: Integrability of polynomial differential systems. In: Canada, A., Drabek, P., Fonda, A. (eds.) Handbook of Differential Equations, Ordinary Differential Equations, vol. 1. Elsevier, Amsterdam (2004). Chapter 5
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Schlomiuk, D.: Algebraic and geometric aspects of the theory of polynomial vector fields. In: Schlomiuk, D. (ed.) Bifurcations and Periodic Orbits of Vector Fields. NATO ASI Series C, vol. 408, pp. 429–467. Kluwer Academic, London (1993)
Metadata
Title
Limit Cycle Bifurcations Near a Center
Authors
Maoan Han
Pei Yu
Copyright Year
2012
Publisher
Springer London
Book
Normal Forms, Melnikov Functions and Bifurcations of Limit Cycles

Print ISBN: 978-1-4471-2917-2

Electronic ISBN: 978-1-4471-2918-9

Copyright Year: 2012

DOI
https://doi.org/10.1007/978-1-4471-2918-9_7

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