Stable limit cycle

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。

The sufficient conditions of nonexistence of the closed orbit and conditions of existence of the unique and stable limit cycle are also obtained .

讨论了系统平衡点的性态，给出了系统无闭轨的充分条件以及存在惟一稳定极限环的条件。

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。

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。

It is mathematically and thoroughly proved in this paper that the nonlinear stochastic ocean-atmosphere oscillator model possesses a stable limit cycle ;

从数学上严格证明了非线性随机海-气振荡子模型存在一个稳定的极限环；

It proves that steering shimmy is a vibration phenomenon of stable limit cycle occurring after Hopf bifurcation , which is elaborated by theories of ordinary differential equation and nonlinear dynamics .

以常微分方程稳定性理论和非线性动力学理论为基础，阐明了自激型摆振是一种非线性动力学Hopf分岔后出现的稳定极限环振动现象。

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。

In this paper we first prove an inference of the principle of the annular domain , then using the inference , we can infer that . ( 1 ) differential system ( 2 ) has a stable limit cycle ;

本文给出环区原理在三维空间中的一个推论，它证明了满足三个条件的空间系统就满足环区原理的条件，从而存在周期轨道。

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°；

In this paper we study a model of plant-herbivore systems . Sufficient and necessary conditions for the globally asymptotic stability of the positive equilibrium points and for the existence of unique stable limit cycle are obtained . We have also obtained a global bifurcation curved surface .

本文研究了一个植物&食植者系统模型，得到了正平衡点全局渐近稳定及存在唯一稳定极限环的充分必要条件，且得到了一个全局分支曲面。

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 supercritical or subcritical Hopf bifurcations are founded in the airfoil flutter system , i.e. the system has stable or unstable limit cycle oscillations motion .

通过分析发现系统中存在超临界（亚临界）Hopf分岔，即系统会发生稳定（不稳定）的极限环颤振运动。