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Limit Cycle Bifurcations of a Cubic Polynomial System via Melnikov Analysis
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KeyWord
:
Boussinesq equation, vacuum, global strong solution, exponential decay-in-time
Author Name
Affiliation
Peixing Yang
School of Mathematical Sciences
,
CMA-Shanghai
,
Shanghai Jiao Tong University
,
Shanghai 200240
,
China.
Jiang Yu
School of Mathematical Sciences
,
CMA-Shanghai
,
Shanghai Jiao Tong University
,
Shanghai 200240
,
China.
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Abstract
:
In this paper, a linear perturbation up to any order in $\epsilon$ for a cubic center with a multiple line of critical points is considered. By the algorithm of any order Melnikov function, the sharp upper bound of the number of limit cycles is 2.
