| 二维非线性动力系统的多极限环分叉的参数控制 |
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| 引用本文： | 李静,缪素芬.二维非线性动力系统的多极限环分叉的参数控制[J].数学杂志,2005,25(6):695-700. |
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| 作者姓名： | 李静 缪素芬 |
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| 作者单位： | 北京工业大学应用数理学院,北京,100022 |
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| 摘 要： | 本文研究了一类具有Z2-等变性质的5次扰动平面Hamilton向量场，利用动力系统的分叉理论和判定函数法，通过控制其参数，得到系统在两组不同的参数条件下分别存在20和23个极限环，以及它们之间相对位置的不同构型.这一结果对机械振动中相应的控制问题有理论指导意义。
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| 关 键 词： | 非线性动力系统 多重极限环 Hamilton系统 判定函数 |
| 文章编号： | 0255-7797（2005）06-0695-06 |
| 收稿时间： | 2005-06-03 |
| 修稿时间： | 2005-06-032005-10-11 |
THE PARAMETER CONTROL FOR THE MULTIPLE LIMIT CYCLES BIFURCATION ON A TWO DIMENSIONAL NONLINEAR DYNAMICAL SYSTEM |
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| Li Jing,Miao Su-fen.THE PARAMETER CONTROL FOR THE MULTIPLE LIMIT CYCLES BIFURCATION ON A TWO DIMENSIONAL NONLINEAR DYNAMICAL SYSTEM[J].Journal of Mathematics,2005,25(6):695-700. |
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| Authors: | Li Jing Miao Su-fen |
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| Institution: | College of Applied Sciences, Beijing University of Technology, Beijing 100022, China |
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| Abstract: | In this paper, we consider a Z2-equivariant perturbed polynomial Hamiltonian system of degree 5. By using the bifurcation theory of planar dynamical system and the method of detection function, we control the parameters to obtain 20 and 23 limit cycles under two different control conditions and the configurations of compound eyes are also obtained. This result may serve as theoretical reference for the control problem in mechanical oscillation. |
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| Keywords: | nonlinear dynamic system multiple limit cycles Hamiltonlan system detection functions |
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