| 具有参数激励约简的扰动KdV方程的混沌行为 |
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| 作者姓名： | 周良强 陈芳启 陈予恕 |
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| 作者单位： | [1]南京航空航天大学航空宇航学院,中国南京210016 [2]南京航空航天大学理学院,中国南京210016 [3]天滓大学机械工程学院,中国天津300072 |
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| 基金项目： | 国家自然科学基金
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江苏省自然科学基金 |
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| 摘 要： | 研究了具有参数激励约简的扰动KdV方程的混沌动力学行为.利用改进的Melnikov方法分析了由于同宿轨道的横截相交而产生的混沌行为.对周期外激励、周期线性参数激励和周期非线性参数激励下的扰动KdV方程的混沌行为进行了比较,发现划分混沌区与非混沌区的临界曲线是互不相同的.尤其是对非线性参数激励系统,存在"死频率".当这类系统受到该频率激励时,不论激励的振幅多大,混沌也不会发生.用时间积分法对上述系统进行了数值计算,结果与理论分析一致.
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| 关 键 词： | KdV方程 混沌行为 Melnikov方法 Korteweg-de Vries equation chaotic behavior Melnikov method 参数激励 约简 扰动 方程 混沌行为 PARAMETRIC EXCITATION FORM KdV EQUATION REDUCTION BEHAVIOR Numerical results analytical time integration scheme used find numerical solutions chaos matter |
| 修稿时间： | 2007/1/5 0:00:00 |
CHAOTIC BEHAVIOR ON REDUCTION OF PERTURBED KdV EQUATION IN FORM OF PARAMETRIC EXCITATION |
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| Authors: | Zhou Liangqiang Chen Fangqi Chen Yushu |
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| Abstract: | The chaotic dynamic behaviors of a reduction of perturbed Korteweg-de Vries (KdV) equation in form of a parametric excitation are studied. Chaotic behaviors from homoclinic crossings are analyzed with an improved Melnikov method and are compared for the systems with a periodically external excitation, with a linear periodically parametric excitation, or with a nonlinear periodically excitation. The critical curves separating chaotic regions and non-chaotic regions of the above systems are different from each other. Especially, a dead frequency is presented for the system with a nonlinear periodically parametric excitation. The chaos excited at the frequency does not occur no matter how large the excitation amplitude is. A time integration scheme is used to find the numerical solutions of these systems. Numerical results agree with the analytical ones. |
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| Keywords: | Korteweg-de Vries equation chaotic behavior Melnikov method |
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