LIMIT CYCLE BIFURCATIONS IN NEAR-HAMILTONIAN SYSTEMS BY PERTURBING A NILPOTENT CENTER
2008 ◽
Vol 18
(10)
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pp. 3013-3027
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Keyword(s):
As we know, Hopf bifurcation is an important part of bifurcation theory of dynamical systems. Almost all known works are concerned with the bifurcation and number of limit cycles near a nondegenerate focus or center. In the present paper, we study a general near-Hamiltonian system on the plane whose unperturbed system has a nilpotent center. We obtain an expansion for the first order Melnikov function near the center together with a computing method for the first coefficients. Using these coefficients, we obtain a new bifurcation theorem concerning the limit cycle bifurcation near the nilpotent center. An interesting application example & a cubic system having five limit cycles & is also presented.
2012 ◽
Vol 22
(12)
◽
pp. 1250296
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2020 ◽
Vol 30
(09)
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pp. 2050126
Keyword(s):
Keyword(s):
Keyword(s):
Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
◽
pp. 1650204
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Keyword(s):
2008 ◽
Vol 132
(3)
◽
pp. 182-193
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2021 ◽
Vol 31
(09)
◽
pp. 2150123
Keyword(s):
2018 ◽
Vol 28
(02)
◽
pp. 1850026
2019 ◽
Vol 29
(12)
◽
pp. 1950160
2015 ◽
Vol 25
(06)
◽
pp. 1550080
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