同宿

In chapter two, we study the problems of bifurcation and stability of homo-clinic loop with higher dimensions.

第二章我们研究高维系统同宿环的分支与稳定性问题。

When and we show that system (1) has the cusp bifurcation of codimension 2(ie,Bogdanov-Takens bifurcation); when ,we show that this system has the cusp bifurcation with codimension at least S.

而且我们选择了系统的原参数中的二个作为分支参数，可以使系统(1)进行Bogdanov-Takens余维2普适开折，从而证明系统(1)同宿轨的存在性。

Double homoclinic loops; Resonant eigenvalues; Nontwist; Periodic orbit; Bifurcation; Periodic solution; Predator-prey system; Fixed point theorem; Coincidence degree; Delay; Functional response function

基础科学，数学，动力系统理论双同宿环；共振特征根；非扭曲；周期轨；分支；周期解；捕食者-食饵系统；不动点定理；重合度；时滞；功能反应函数

Based on the equilibrium equation of an arch element the cubic nonlinear dynamic model with second order is established and the nonlinear differential dynamic system without constant term is obtained through a transfer process of T=U+b. Hence three fixed points and the homoclinic orbits are found. The critical condition of the chaotic vibration of the elastic arch is given by using the method of Melnikov function. The numerical results of the stationary and chaotic motion are given and discussed.

首先利用拱的单元平衡方程建立了拱的二阶三次非线性动力学模型；然后通过变换使方程转化为不含常数项的非线性微分动力系统，并由此得到无扰动系统的3个不动点与同宿轨道；再用Melnikov函数法给出了发生混沌的临界条件；最后给出了该系统出现定常运动和混沌运动的数值结果。

In chapter 1,we find out a kind of two-parameter invariant cubic curve family of a certainquadratic system which is important one for studying the distribution of limit cycles.

第二章讨论一般的二次系统具有三次代数曲线同宿环的充要条件，针对问题，我们采用了具有双曲鞍点的二次系统的标准形，利用仿射坐标变换，我们把系统和曲线同时简化，使问题得到了完满解决。

In Chapter 2, an autonomous perturbation of a class of planar Hamiltonian systems with homoclinic orbits is discussed.

第二章讨论了一类含有同宿轨的平面Hamilton系统的自治扰动。

By measuring the distance between the stable manifold and the unstable manifold of the hyperbolic fixed point in the Poincare map, it is shown whether the system has transversaUy homoclinicpoints and chaos in the sense of Smale horseshoes.

Melnikov方法是用来判定一个系统是否存在Smale马蹄意义下的混沌的一种有效的数学方法，它通过测量Poincare映射的双曲不动点的稳定流形与不稳定流形之间的距离来判定系统横截同宿点的存在性及Smale马蹄意义下的混沌的存在性。

One important feature ofHamiltonian systems is that it has energy(its energic function is Hamiltonian func-tion),then,its solutions on 2-dimensional plane are some contour lines,the points onstable manifold emanating from hyperbolic equilibrium point have the same energyas that on unstable manifold,then,one can guess that they form a closed curve,i.e.homoclinic orbits under certain conditions,and the contour lines in the innerpart of homoclinic orbit are periodic orbits.

哈氏系统的一个重要特征是它有能量存在(以Hamiltonian函数作为它的能量)，那么在二维平面上，它的解表现为一些等值线，从双曲平衡点发出的稳定流形和不稳定流形上的点具有相同的能量，那么可以猜测，在一定条件下它们构成一条封闭的曲线，即同宿轨，而且其内部的等值线都是周期轨道。

Meantime, the inexistence of the large 2-hom loop and large 2-per orbit are also demonstrated.

同时，我们还证明了大2-同宿环和大2-周期轨的不存在性。

In chapter 3,we dig out two families of invariant quartic curves of a quadratic system.

第五章讨论向量场具有对称中心的二次系统，利用系统的不变双曲线及不变四次曲线，我们确定了一个对应极限环（1.1）分布的二维参数区域，其边界的构成为如下几种常见的极限环分枝：霍夫分析，庞加莱分枝，同宿分枝和异宿分枝。

I am accused of being overreligious," she said in her quiet, frank manner,"but that does not prevent me thinking the children very cruel who obstinately commit such suicide.""

客人们在卡罗利娜·埃凯家里，举止就文雅一些，因为卡罗利娜的母亲治家很严厉。

Designed by French fashion house Herm è s, this elegant uniform was manufactured in our home, Hong Kong, and was the first without a hat.

由著名品牌 Herm è s 设计，这件高贵的制服是香港本土制造，是我们第一套不配帽子的制服。