极限环

The number and stability of the limit cycles of a class of polynomial system with degree n are studied under some conditions by means of the results about Abel equation.

并利用关于Abel方程的这些结果得到了一类n次多项式系统在一定条件下极限环的个数和稳定性。

In the fourth chapter, some general equations are studied, of which Abel equation and some equations that have been intensively studied are the special cases.

第三章利用Abel方程已有的结果来讨论多项式系统的极限环的存在性，个数和稳定性，推广了水树良和蔡燧林的相关工作。

Using affine coordinate transformation,we simplifytogether the system and the curve.

我们得到了一批关于极限环存在性的便于应用的结果。

The paper is devoted to the quartic invariant algebraic curves in quadratic system.

本文在给定参数满足一定的条件下，研究了一类二次系统的四次不变代数曲线系统平衡点的稳定性态，并运用Dulac函数法给出了该系统不存在极限环的充分条件，这一研究在同类问题中具有一定的拓展性。

Therefore, alogical generalization of limit cycle in stochastic models needs to be developed, andinterestingly, the concept of circulation in the mathematical theory of nonequilibriumsteady states [91] actually plays the role.

因此，需要研究随机模型中对应于确定性模型极限环概念的合理推广；而在关于开系统非平衡定态的数学理论[91]中，环流恰好可以扮演这样一个角色。

According to the change of the enemy\'s quantity and the qualitative theory of the differential equation, we research the spruce aphides and its predator system. At the same time, we discussion the spruce aphid multiplication model when the natural enemy quantity is a certain value and the periodic oscillating model whose the quantity of the natural enemy changes along with the time. Obtains the stability condition of the balance point and the limit-cycle existing condition, the system presents the dissipative structure\'s character. Finally it explains that this theoretical analysis has certain practical significance regarding the preventing and controlling harmful insect.

第五章，松毛虫与其天敌的关系是食饵和捕食者的关系，根据天敌数量的变化，利用微分方程定性理论，研究松毛虫与天敌系统，讨论天敌数量为一定时的松毛虫增殖模型和天敌数量随时间变化的周期振荡模型，得到正平衡点全局稳定性和极限环的存在条件，通过计算机模拟，说明周期振荡的捕食模型能够呈现典型的时间耗散结构特征，对于防治害虫有一定的实际意义。

Both single and double-stable limit cycle flutter states are found in wind-tunnel test. And the conclusion is proofed that the equivalent linearization based on the second order asymptotic solution of KBM method is more accurate than that based on the first order one, which is equivalent to the conventional harmonic balance method.

风洞实验时，吹出了单、双稳定极限环颤振情形，并验证了基于KBM二次渐近解的当量线化分析比KBM法一次渐近解的当量线化分析要精确一些的结论。

The key idea is to reduce the global stability problem to the asymptotic stability of an uncertain discrete-time system.

主要思想是将所研究的极限环的全局稳定性问题转化为不确定离散系统的渐近稳定性问题。

In the second chapter, we consider a kind of Kolmogorov system. The sufficient condition for nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained by using divergence integral, Poincare-Bendixson theorem and Zhang Zhifen\'unique theorem.

第二章讨论了一类Kolmogorov系统，利用发散量积分、环域定理和张芷芬唯一性定理，得到了该系统无闭轨的充分条件和存在唯一极限环的条件。

With the increase of angle of attack, the types and connection models of singular point will be changed.

随着降落伞迎角增大，奇点类型和奇点间的连接方式将发生改变，降落伞物面附近的涡环里将出现极限环，截面流场中将出现新的鞍点和结点。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。