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。
Furthermore, the condition for the existence of stable limit cycle was discussed.
机器人稳定行走周期步态在相平面内表现为极限环，讨论了其存在的条件。
When the value of critical threshold larger than 1, the disease and insect pests equilibrium point is locally asymptotically stable An appropriate Dulac function should be choosed and Bendixson-Dulac creterion is used to prove that the limit cycle in this model does not exist. It explains that the disease and insect pests equilibrium point is globally asymptotically stable.
选取适当的Dulac函数，利用Bendixson-Dulac判别法证明了极限环的不存在性，说明局部渐近稳定的病虫害平衡点也全局渐近稳定。
In the second chapter, we consider a kind of Kolmogorov system. The sufficient conditions of nonexistence of the closed orbit and existence of the unique and stable limit cycle are obtained.
第二章讨论了一类Kolmogorov系统，得到了系统无闭轨的充分条件和存在唯一稳定极限环的条件，推广了颜向平，张存华等的结果。
At a given series compensation level, the original sub-synchronous resonance may change into stable limit cycle.
在某一串联补偿度上，出现的次同步谐振可能被轨道稳定的极限环所取代。
In other words, the unstable limit cycle will be bifurcated from the original asymptotical stable equilibrium point at another higher series compensation level, and the system dynamics will change.
换句话说，在另一较高的串联补偿度上，轨道不稳定的极限环将从原来渐近稳定平衡点上分岔出来，系统的稳定性态将被改变。
The result shows that the stability solution of the system transform from the stable equilibrium point to the limit cycle oscillatory after multiple cycle bifurcation, and it transforms to the quasi-periodic oscillation after Hopf bifurcation.
系统由稳定的平衡点通过倍周期分岔收敛到稳定的极限环运动，由Hopf分岔转化为概周期运动。
It is not satisfied general condition for existence of a stable limit cycle.
给出了其极限环存在性、唯一性以及稳定性的证明。
Simulation results show that a stable limit cycle of dynamic walking is achieved, and the control strategy is feasible.
仿真实验表明，动态步行渐进收敛于稳定的极限环，控制算法是可行的。
The conditions were given to ensure the system has stable limit cycle and unstable limit cycle, respectively.
给出了系统分别存在稳定极限环和不稳定极限环的条件。
On the Fatigue Limit of the Mechanical Material under the Stable Alternative Stress with an Arbitrary Cycle Characteristic
机械材料在任意循环特征稳定交变应力作用下的疲劳极限
And the simulation results of hunting derailment indicates that there is a derailment critical velocity which corresponds to the maximal stable limit cycle during hunting for wheel-rail system, any weak excitation will induce a derailment if the running velocity exceeds the derailment critical velocity.
通过对单轮对蛇行脱轨机理的研究表明，轮轨系统存在脱轨临界速度，最大蛇行稳定极限环对应于脱轨临界速度，当运行速度超过脱轨临界速度时，任何微弱激扰将可能导致脱轨。
The results indicate that when the speed reaches 46.14 km/h, supercritical Hopf bifurcation occurs to the system and stable limit cycle appears, i. e. wheels oscillates around the kingpin at the equal amplitude, which can maximize 2.982 °;
结果表明：当车速达到46.14km/h，系数发生了超临界Hopf分岔，出现了稳定的极限环，即车轮绕主销开始作稳定的等幅摆动，极限环的幅值最大达到2.982°；
Based on experimental results, both equivalent linearization and numerical simulation methods are performed to investigate the double stable limit cycle flutter characters of a two dimensional wing with preloaded free-play nonlinear pitching stiffness.
本文利用等效线化及数值计算方法，研究了带初偏间隙型非线性俯仰刚度的二元颤振系统的双稳态极限环颤振特性，给出了极限环稳定区间的稳定性判据。
The results indicate that when the speed reaches 46.14 km / h, supercritical Hopf bifurcation occurs to the system and stable limit cycle appears, i.e. wheels oscillates around the kingpin at the equal amplitude, which can maximize 2.982 °;
结果表明：当车速达到46.14km/h，系数发生了超临界Hopf分岔，出现了稳定的极限环，即车轮绕主销开始作稳定的等幅摆动，极限环的幅值最大达到2.982°；