| 1. | Application of melnikov method in the study of chaotic motions of pipe conveying fluid
简谐激励下输流管动态响应特性的实验研究 |
| 2. | Theoretical analysis manifested that the boundedness condition contained the famous melnikov criteria of chaos
理论分析表明，解的有界性条件包含了melnikov函数为零的混沌判据。 |
| 3. | By using melnikov method , the melnikov function of homoclinic orbit or heteroclinic orbit is calculated and established
应用melnikov方法，计算并建立了同宿轨道或异宿轨道的melnikov函数。 |
| 4. | The melnikov function of subharmonic orbits is calculated and established and the criterion of appearing periodical m point of poincare mapping is presented . 4
计算并建立了次谐周期轨道的melnikov函数，给出了poincare映射出现周期m点的判据。 |
| 5. | By use of the direct perturbation method , perturbed correction is construct and its boundedness conditions are established that contain the melnikov criterion for the onset of chaos
运用直接微扰法，我们给出了一级微扰方程的解析解及其有界性条件。 |
| 6. | More specifically , we combine geometric singular perturbation theory with melnikov analysis and integrable theory to prove the persistence of homoclinic orbits
) dinger方程同宿轨道的存在性，其基本思想方法是基于整体可积理论、 melnikov方法和奇异扰动理论的综合运用 |
| 7. | One is the stochastic extended form of the high - dimension melnikov method which make it possible to choose proper noise excitation to extend the chaos window of a dynamical system
一是提出了一种高维随机梅尔尼科夫推广方法，这一方法使得我们顺利利用合适的噪声扩大系统混沌窗口成为可能。 |
| 8. | In the fourth chapter , on the basis of the second and third chapter , using the melnikov function approach , we find the conditions for producing chaotic josephson effects and obtain the critertia for the chaos
在第二章和第三章的基础上，第四章主要研究了阻尼条件下的正常和混沌的josephson效应。利用melnikov函数方法给出了混沌的参数区域。 |
| 9. | Meanwhile , we analyze the procession of the route from the periodic motion to chaos motion of cable via period - doubling bifurcation . in chapter 5 , the chaotic motion of cable is studied by utilizing melnikov method and simulates the chaotic motion digitally
在第五章中，针对第四章得到的结论，用melnikov方法研究了斜拉索的混沌运动，并对斜拉索的混沌运动进行了数值模拟。 |
| 10. | We adopt a three mode fourier truncation and get a six dimensional model . this model is considered and the persistence of the homoclinic orbits is obtained by melnikov ' s analysis together with the geometrical singular perturbation theory
) dinger ( dnls )方程，通过采用三模fourier截断，我们得到一个六维模型，利用melnikov分析和几何奇异扰动理论证明了这个六维模型同宿轨道的保持性。 |
