次极限

In this paper, we discuss the uniqueness limit cycle and the question of bifurcate about a class of general Liénard equation in the system .

当二次系统添加一个三次项变为三次系统后，这两个系统在原点附近的极限环的变化情况是否存在某种联系，亦是一个十分有趣的问题。

Chapter 5 concerns the number of limit cycles for a cubic Hamiltonian system under cubic perturbation.

第五章给出了只关于一个轴对称的三次哈密顿系统的分类，研究了三次哈密顿系统在三次扰动下的极限环的个数与分布。

The integrability conditions and coefficient conditions for the appearance of 5 and 6 limit cycles from the neighborhood of the equator are obtained. An example of cubic system with 6 limit cycles bifurcating from the equator is given for the first time.

同时计算出系统的前6个赤道环量，得到了系统在赤道邻域的可积性条件及在赤道附近分支出5个和6个极限环的系数条件，从而首次给出了一个平面三次系统在赤道附近分支出6个极限环的计算实例。

The relation between the limit state function of large and complex structural systems and input random parameters is always unknown. A quadratic polynomial is considered to simulate the physical limit state function.

工程中大型、复杂结构的极限状态方程与输入随机变量的关系往往是未知的，利用响应面法，用一个二次多项式来模拟结构的极限状态方程。

In Chapter 4, we study the center conditions and the bifurcation of limit cycles at a degenerate singular point as well as that at infinity for a quintic polynomial system and prove that the system has 5 limit cycles around the origin and 2 limit cycles around infinity.

在第三章中，我们分别研究了一类三次多项式系统、一类五次多项式系统、一类七次多项式无穷远点的中心条件与极限环分支问题。

At the same time, the center conditions and bifurcation of limit cycles at the origin of the quintic polynomial system are also investigated.

第二章研究了一类三次多项式系统由细焦点分支出极限环的问题，证明了该系统有12个小振幅极限环，证明过程是符号和代数的，且焦点量的表达式相对简单。

In the region upstream of vortex breakdown, the sectional streamlines emanating from the leading edge spiral inward to primary vortex and in the region downstream of the breakdown, on the other hand, the streamlines separating from the leading edge are not entrained into the vortex core in the instantaneous sense. Along the axis, the topology of the primary vortex alters several times starting from stable focus near the apex to unstable focus, and lasts back to stable focus near wake edge, the stable hmit cycle and unstable limit cycle are shown in this evolution.

发现在截面流线谱中，即使奇点的类型、数目及位置相同，奇点的连接方式也有可能不同；旋涡破裂点前，主涡由来自前缘的力线卷绕而成，主涡焦点与前缘半鞍点相连，旋涡破裂后，来自前缘的力线不再卷入主涡，主涡焦点与对称面上的鞍点相连：在流体由翼尖流向后缘的过程中，截面流线谱的拓扑结构发生了多次变化，主涡焦点相继由稳定状态转变为不稳定状态，最后又转化为稳定状态，并先后出现了稳定的极限环及不稳定极限环。

Our results show that the rate of correlation among the random variables of those output sequences are low although they are not independent; in addition, the output sequences of those combined generators are homogeneous Markov chains which are strictly stationary processes with ergodicity; the output sequences of those combined generators are also proved to summit to the strong law of large numbers and the central limit theorem; finally the computation formula of the rate of the accordance between the output sequences and input sequences of those combined generators is given.

我们的研究结论表明：虽然这些序列中随机变量之间不具有相互独立性，但它们的相关程度却比较低；证明了"停走"生成器，KM_1M_2型组合生成器和加法型组合生成器的概率模型输出序列都是强平稳的和遍历的齐次马氏链；讨论了这些序列的概率极限性质，证明了它们均服从强大数定律和中心极限定理；还分别给出了各类生成器的输出序列与输入序列之间的符合率的计算公式。

The theoretical analysis are verified by numerical simulations.Chapter 3 mainly considers a class of predator-prey model with sublinear functional response function. We deduce some sufficient conditions ensuring stability of equilibrium, nonexistence , existence as well as uniqueness of the limit cycle around the positive equilibrium.

第3章研究了一类食饵为线性密度制约，功能反应函数为次线性函数的食饵-捕食者模型，完整地对模型的平衡点的全局稳定性和极限环的存在惟一性进行了定性分析，得到了该系统不存在闭轨线，正平衡点全局稳定和存在惟一稳定的极限环的充分条件。

This is a first time that the problem of limit cycles bifurcating from a degenerate singular point and from infinity under the synchronous perturbed conditions is investigated.

得到了三次、五次、七次系统分别可以在无穷远点分支出7个、8个、9个大振幅极限环的结论，这几个结果是目前最好的。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。