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Published in:
2012 | OriginalPaper | Chapter
9. Finding More Limit Cycles Using Melnikov Functions
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. 9, an idea for finding more limit cycles is introduced, which combines the bifurcation of limit cycles from centers, homoclinic and heteroclinic loops. A generalized theorem is presented. In particular, two polynomial systems are studied. By using the theorems and results obtained in Chaps. 6–9 it is shown that one system can have seven limit cycles while the other can have five limit cycles.