Journal
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS
Volume 15, Issue 2, Pages 471-479Publisher
SPRINGER BASEL AG
DOI: 10.1007/s12346-015-0179-3
Keywords
Averaging method; Melnikov function; Limit cycle bifurcation
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Funding
- National Natural Science Foundation of China [1271261, 11431008]
- Slovenian Research Agency
- NNSF of China [11271252]
- RFDP of Higher Education of China [20110073110054]
- innovation program of Shanghai Municipal Education Commission [15ZZ012]
- European Community Framework Programme [FP7-PEOPLE-2012-IRSES-316338]
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There is a folklore about the equivalence between the Melnikov method and the averaging method for studying the number of limit cycles, which are bifurcated from the period annulus of planar analytic differential systems. But there is not a published proof. In this short paper, we prove that for any positive integer k, the kth Melnikov function and the kth averaging function, modulo both Melnikov and averaging functions of order less than k, produce the same number of limit cycles of planar analytic (or C-infinity) near-Hamiltonian systems.
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