分岔

It includes the undertermined fundamental frequency approaching zero and the collision of the periodic orbit with the saddle point.

然后分别依据系统的待定固有频率趋于零和周期轨道趋近于鞍点两条途径获得了强非线性振动条件下系统同宿分岔的解析判据。

Furthermore, the periodicity of the phenomena and the route from bifurcation to chaos are also investigated in detail.

同时，详细研究了系统由分岔到混沌的发展过程。

Fourth, we have developed a new hybrid control strategy by combining state feedback and parameter perturbation for controlling period-doubling bifurcations and chaos in discrete nonlinear dynamical systems.

4提出了参数调节和状态反馈的混合控制新方法，有效地实现了离散非线性系统的倍周期分岔控制和混沌控制。

In the study of the nonlinear dynamics, Melnikov function is widely used as a criterion to check whether subharmonic or ultra-subharmonic bifurcation even chaos will occur in a perturbed Hamilton system.

在非线性动力系统的研究中， Melnikov函数被广泛地用来作为微扰哈密顿系统是否发生次谐或超次谐分岔乃至混沌的判据。

An important field in vibration engineering is the dynamics of mechanical systems with piecewise smooth features, such as existing clearance, constraint, friction and hysteresis, It is possible to optimize practical system parameters by investi...

对其分岔与混沌行为的研究为工业实际中含间隙机械系统和冲击振动系统的优化设计提供了理论依据。

The corner-collision bifurcation of piecewise smooth systems is addressed.

推导了零时间不连续映射并给出角点碰撞分岔的分段映射。

The parameter space is included to construct a compound piecewise smooth map by composing previous discontinuity mappings with a Poincarémap for smooth periodic solution.

引入参数空间，将未发生碰撞的周期轨道对应的光滑映射与前面得到的不连续映射复合得到两类擦边分岔的分段映射形式。

Because of switching actions, power-factor- correction Boost converters are essentially piecewise smooth nonlinear systems, which leads to the occurrence of fast-scale bifurcations.

由于开关的动作，功率因数校正(power-factor-correc- tion，PFC) Boost变换器本质上是分段光滑的非线性系统，从而导致快时标分岔的产生。

The unified discrete iterative map model of peak current and valley current controlled buck, boost, and buck-boost converters is established, and the unified piecewise smooth iterative map and their corresponding characteristics equations are also derived.

本文建立了峰值电流和谷值电流控制Buck，Boost，及Buck-Boost变换器的统一离散迭代映射模型，并导出了统一的分段光滑迭代映射方程及特征值方程，通过数值仿真得到了占空比变化时的正、逆分岔图和Lyapunov指数谱。

A point of divergence,especially one of great moment.

转折点分岔点，尤指需要作出重大决择的时刻

I can not make it blossom and suits me

我不能让树为我开花

When temperatures are above approximately 80 °C discolouration of the raceways or rolling elements is a frequent feature.

当温度高于 80 °C 左右时，滚道或滚动元件褪色是很常见的特征。