Hopf and homoclinic bifurcations for near-Hamiltonian systems

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• 作者：Yun Tian ^{ytian22@shnu.edu.cn} ; Maoan Han ; ^{mahan@shnu.edu.cn}
• 关键词：Homoclinic loop ; Hamiltonian system ; Melnikov function ; Limit cycle
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：15 February 2017
• 年：2017
• 卷：262
• 期：4
• 页码：3214-3234
• 全文大小：621 K
• 卷排序：262

文摘

We study homoclinic bifurcation of limit cycles in perturbed planar Hamiltonian systems. Suppose that a homoclinic loop is defined by H=hsH=hs. Our main result is that a new method is established for computing the coefficients of the expansion of Melnikov functions at h=hsh=hs. Then by using those coefficients, more limit cycles would be found around homoclinic loops. An example is also provided to illustrate our method.