Limit cycle bifurcations by perturbing a cuspidal loop in a Hamiltonian system

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• 作者：Maoan Han ; Hong Zang ; Junmin Yang
• 关键词：Cuspidal loop ; Melnikov function ; Limit cycle ; Bifurcation ; Hamiltonian system
• 刊名：Journal of Differential Equations
• 出版年：2009
• 出版时间：1 January 2009
• 年：2009
• 卷：246
• 期：1
• 页码：129-163
• 全文大小：344 K

文摘

In this paper, we first study the analytical property of the first Melnikov function for general Hamiltonian systems exhibiting a cuspidal loop and obtain its expansion at the Hamiltonian value corresponding to the loop. Then by using the first coefficients of the expansion we give some conditions for the perturbed system to have 4, 5 or 6 limit cycles in a neighborhood of loop. As an application of our main results, we consider some polynomial Lienard systems and find 4, 5 or 6 limit cycles.