平衡点

The contents of this dissertation include the existence of equeilibrium and the stability criterion about the non-linear kinetic system.

本文的主要内容包括非线性动力系统平衡点的存在性和稳定性条件，并以该系统为主要约束，建立了非线性最优控制模型并证明了最优解的存在性。

Analysis with numerical simulation shows that the equilibrium may not change its stability at all or changes its stability up to a finite number of times.

研究表明，系统在不同参数控制下，平衡点的稳定性可以不发生改变，也可以发生多次稳定性切换。

If , the disease-free equilibrium is globally stable and the disease always dies out.

如果无病平衡点是全局稳定和疾病总是熄灭。

The solution method of the stable equilibrium and the synchronous equilibrium for network preserving model is also provided.

提供了在网络结构保持模型下求解事故后稳定平衡点的电流型方法，从而提供了事故后结局分析的一种有效手段，为暂态稳定分析奠定了基础。

To implement this function, it must be a complete stable network, namely, its all output tracks must converge at a stable equilibrium point.

它为了完成这个功能，它必须是一个完全稳定的网络，即所有输出轨迹必须收敛到一个稳定的平衡点。

In the first section of the part three, the criteria for globally stable equilibrium in n-dimensional predator-prey model are obtained.

第三部分对生态问题的研究第一节利用二次型理论研究了一类n维环状自治系统有密度制约模型，得到了判别此类系统稳定平衡点的充分条件。

Although the unstable manifold of the fast subsystem is different from that of the full system, the stable manifold of the fast subsystem is almost the same as that of the full system, so the domain of attractor of the full system can be given by that of the fast subsystem.

除了理论分析外，同时也给出了数值模拟的结果，包括分支图，轨线，吸引域，各变量的收敛性等。本章给出的稳定平衡点的吸引域对电力系统实行适时控制起到很重要的作用。

The stability of system equilibrium point and the existence condition of 3-D Hopf bifurcation as well as the stability of hence generated periodic solution were analyzed, so that the existence of limit cycles on the two-dimensional stable manifold of one microbial species and its nutrition was verified when other one had the disadvantage in the competition so as to become extinct.

研究当营养消耗率δ1＝δ1为一般的非减连续函数和δ2＝常数的三维Chemostat模型，分析系统平衡点的稳定性，三维系统经历Hopf分支的条件和由此产生的周期解的德定性，证明系统中某一微生物物种处于竞争劣势而趋于灭绝时另一微生物物种和营养的二维稳定流形上极限环的存在性。

The stability of system equilibrium point and the existence condition of 3-D Hopf bifurcation as well as the stability of hence generated periodic solution were analyzed,so that the existence of limit cycles on the two-dimensional stable manifold of one microbial species and its nutrition was verified when other one had the disadvantage in the competiti.

研究当营养消耗率1δ=1δ为一般的非减连续函数和2δ=常数的三维Chemostat模型，分析系统平衡点的稳定性，三维系统经历Hopf分支的条件和由此产生的周期解的稳定性，证明系统中某一微生物物种处于竞争劣势而趋于灭绝时另一微生物物种和营养的二维稳定流形上极限环的存在性。

A simple form of the unstable manifold s for the fixed points not being on the boundary;2. Aim To study singular points, closed orbits, stable manifolds and unstable manifold s of a second order autonomous Birkhoff system.

目的研究二阶Birkhoff自治系统的奇点、闭轨、稳定流形与不稳定流形，方法用常1微分方程的定性方法进行研究，结果与结论给出二阶Birkhoff自治系统的奇点判据、闭轨判据、双曲平衡点判据，得到与其相关的平衡稳定性、稳定流形与不稳定流形等。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。