ASYMPTOTIC EXPANSIONS OF MELNIKOV FUNCTIONS AND LIMIT CYCLE BIFURCATIONS
2012 ◽
Vol 22
(12)
◽
pp. 1250296
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Keyword(s):
In the study of the perturbation of Hamiltonian systems, the first order Melnikov functions play an important role. By finding its zeros, we can find limit cycles. By analyzing its analytical property, we can find its zeros. The main purpose of this article is to summarize some methods to find its zeros near a Hamiltonian value corresponding to an elementary center, nilpotent center or a homoclinic or heteroclinic loop with hyperbolic saddles or nilpotent critical points through the asymptotic expansions of the Melnikov function at these values. We present a series of results on the limit cycle bifurcation by using the first coefficients of the asymptotic expansions.
2020 ◽
Vol 30
(09)
◽
pp. 2050126
Keyword(s):
Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
◽
pp. 1650204
◽
Keyword(s):
2008 ◽
Vol 18
(10)
◽
pp. 3013-3027
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Keyword(s):
2016 ◽
Vol 26
(11)
◽
pp. 1650180
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2018 ◽
Vol 28
(03)
◽
pp. 1850038
2015 ◽
Vol 25
(06)
◽
pp. 1550083
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Keyword(s):
Keyword(s):
Keyword(s):
2008 ◽
Vol 132
(3)
◽
pp. 182-193
◽
2018 ◽
Vol 28
(02)
◽
pp. 1850026