| 摘要: |
| 考虑未扰Liénard系统ẋ=y，ẏ=-g（x），其中deg g（x）=7，当该系统分别含有2，3，4和5个奇点时，给出了其所有的不同拓扑类型的相图，并给出了Melnikov函数在含有2个幂零尖点和1个双曲鞍点的双异宿环附近的展开式和得到极限环的条件. |
| 关键词: 极限环 Liénard系统 近哈密顿系统 异宿环 Melnikov函数 |
| DOI：10.3969/J.ISSN.1000-5137.2020.03.006 |
| 分类号:O193 |
| 基金项目:The Natural Science Foundation of China (11971145); The Natural Science Foundation of Hebei Province(A2019205133) |
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| On the expansion of the Melnikov function near a double heteroclinic loop with two nilpotent cusps |
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MIAO Jiale, YANG Junmin
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School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, Hebei, China
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| Abstract: |
| In this paper, we give all the different topological types of phase portrait for the unperturbed Liénard system ẋ=y, ẏ=-g(x) in the case that deg g(x)=7 and the system has 2, 3, 4 and 5 singular points, respectively. We then give the expansion of Melnikov function near a double heteroclinic loop with two nilpotent cusps and one hyperbolic saddle. We also give the conditions to obtain the limit cycles. |
| Key words: limit cycle Liénard system near-Hamiltonian system heteroclinic loop Melnikov function |
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