| 一类Mathieu对方程的分叉性和复杂性 |
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| 引用本文： | 吴锋民,张存元,范竞藩.一类Mathieu对方程的分叉性和复杂性[J].浙江大学学报(理学版),1995(2). |
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| 作者姓名： | 吴锋民 张存元 范竞藩 |
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| 作者单位： | 浙江工业大学!杭州310014物理系在职研究生(吴锋民)，浙江工业大学!杭州310014(张存元，范竞藩) |
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| 摘 要： | 用理论和数值计算方法对一类Mathieu方程进行了研究.发现该振动系统存在着广泛的周期分叉、混沌行为、对称性、“跳跃”现象、“放大”和“缩小”现象等一系列复杂的行为,并对调整系统参量以改变系统运动性态的问题作了初步的探讨.
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| 关 键 词： | Mathieu方程 Melnikov方法 周期分叉 :混沌 对称性 相图 |
Bifurcation and Complicated Property in a Kind of Mathieu Equation |
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| Wu Fengmin Zhang Cunyun Fan Jingfan.Bifurcation and Complicated Property in a Kind of Mathieu Equation[J].Journal of Zhejiang University(Sciences Edition),1995(2). |
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| Authors: | Wu Fengmin Zhang Cunyun Fan Jingfan |
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| Abstract: | A kind of Mathieu equation is studied by theoretical and numerical method. It is found that there are a lot of complicated behaviors in this system, i. e. period bifurcation, chaotic behaviors, symmetry, jump phenomena, amplification and shinkage phenomena, etc. In addition, the problem of changing the character of the system with adjusting parameters is discussed briefly. |
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| Keywords: | Mathieu equation Melnikov method periodic bifurcation chaos symmetry phase portrait |
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