Limit cycle bifurcation by perturbing a cuspidal loop of order 2 in a Hamiltonian system

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• 作者：Ali Atabaigi ^{aelmi@math.iut.ac.ir} ; Hamid R.Z. Zangeneh ; ^{hamidz@math.iut.ac.ir} ; ^{hamidz@cc.iut.ac.ir} ; Rasool Kazemi ^{r.kazemi@math.iut.ac.ir}
• 关键词：34C07 ; 34C08 ; 37G15 ; 34M50
• 刊名：Nonlinear Analysis
• 出版年：2012
• 出版时间：March 2012
• 年：2012
• 卷：75
• 期：4
• 页码：1945-1958
• 全文大小：319 K

文摘

This paper deals with the analytical property of the first Melnikov function for general Hamiltonian systems possessing a cuspidal loop of order 2 and its expansion at the Hamiltonian value corresponding to the loop. The explicit formulas for the first coefficients of the expansion have been given. We prove that at least 13 limit cycles can bifurcate from the cuspidal loop of order 2 under certain conditions. Then we consider the cyclicity of a cuspidal loop in some Li¨¦nard and Hamiltonian systems, and determine the number of limit cycles that can bifurcate from the perturbed system.