| 平面折射系统极限环的存在和唯一性 |
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| 引用本文： | 李时敏,陈挺,刘玉记,黎小丽.平面折射系统极限环的存在和唯一性[J].中国科学:数学,2021(4):605-614. |
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| 作者姓名： | 李时敏 陈挺 刘玉记 黎小丽 |
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| 作者单位： | 广东财经大学统计与数学学院 |
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| 基金项目： | 广州市科技计划(批准号:201707010426和20180401350);广东省自然科学基金(批准号:2017A030313010);国家自然科学基金(批准号:11771059)资助项目。 |
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| 摘 要： | 本文考虑平面折射系统的极限环个数问题.根据左、右子系统的动力学性态,可以将其分为如下6种类型:焦点-焦点、焦点-鞍点、焦点-结点、鞍点-鞍点、鞍点-结点和结点-结点.利用Poincaré映射,本文证明折射系统为焦点-结点情形时最多存在1个极限环.
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| 关 键 词： | 极限环 分段线性系统 折射系统 |
On the existence and uniqueness of limit cycles in planar refracted systems |
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| Shimin Li,Ting Chen,Yuji Liu,Xiaoli Li.On the existence and uniqueness of limit cycles in planar refracted systems[J].Scientia Sinica Mathemation,2021(4):605-614. |
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| Authors: | Shimin Li Ting Chen Yuji Liu Xiaoli Li |
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| Abstract: | This paper investigates the number of limit cycles in planar refracted systems. According to the dynamics of the left and right subsystems, we can divide them into the following six types: focus-focus, focus-saddle,focus-node, saddle-saddle, saddle-node and node-node. Using the Poincar′e map, we prove that the refracted systems have at most one limit cycle with focus-node type. |
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| Keywords: | limit cycle piecewise linear systems refracted systems |
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