period doubling bifurcation

The results show that the motion of the rotor undergoes complicated nonlinear dynamics phenomena , such as period doubling bifurcation , tangent bifurcation and secondary Hopf bifurcation .

结果表明，转子运动呈现倍周期分叉、切分叉和二次Hopf分叉等复杂的非线性动力学现象。

Results : When the pacing interval ( PI ) shortened , the cycle length ( CL ) showed alternation , period doubling bifurcation , and quasiperiodicity , which were nonlinear dynamics properties and chaotic patterns .

结果：在心室颤动发生前及过程中，激动周期（CL）出现了交替节律、倍周期分叉及准周期等非线性动力学特性；

Analysis of period doubling bifurcation in power system

电力系统倍周期分岔分析

Study on period doubling bifurcation based on systematic Lyapunov exponent analysis

基于系统Lyapunov指数分析的倍周期分岔研究

Numerical Conditions for Period Doubling Bifurcation and Stability of Periodic Responses

倍周期分岔及解稳定性的数值条件研究

Simulation Study of Period Doubling Bifurcation in Buck Converters Using Harmonic Balance

利用谐波平衡法对Buck变换器中倍周期分岔的仿真研究

Period Doubling Bifurcation and Its Stability Analysis for a Class of Planar Map

平面映射一类不动点的倍周期分支及其稳定性判定

A Method to Calculate Period Doubling Bifurcation

计算倍分叉的一种方法

The Numerical Simulation of Period Doubling Bifurcation and Chaos in a Two Degree of Freedom Dry Friction System

一类两自由度干摩擦系统倍化分岔与混沌的数值模拟

The main route to chaos for this rotor system is the period doubling bifurcation cascade .

转子系统进入混沌的主要途径是倍周期分岔。

Influences of Period Doubling Bifurcation and Torus Bifurcation on the Voltage Stability of a Typical Power System

倍周期分岔和环面分岔对电力系统电压稳定性的影响

There exists period doubling bifurcation and chaos .

存在着倍周期分叉现象和混沌运动。

Using the condition for bifurcation , a feedforward control is designed that eliminates a period doubling bifurcation .

基于这个分岔条件，可以设计一个前馈控制来避免倍周期分岔的发生。

The PDB ( Period Doubling Bifurcation ) and chaos phenomenon may threaten the security and stability of electric power system .

电力系统中倍周期分岔PDB（PeriodDoublingBifurcation）和混沌现象将影响系统安全稳定运行。

With changes of parameters , besides stable periodic motion the system will lead to chaotic motion by ways of period doubling bifurcation and Hopf bifurcation .

在一定的参数条件下，系统除了存在稳定的周期运动形态之外，还存在着倍周期分叉、Hopf分叉以及其他分叉，系统会沿着倍周期分叉、Hopf分叉等多种途径进入混沌运动。

Two criteria for determining the critical parameter values of period doubling bifurcation or Hopf bifurcation of a general four dimension mapping system are presented in this paper .

本文分别研究了含多参数的四维映射系统的周期倍化分叉和Hopf分叉的参数临界值的代数判据。

In this paper , based on the harmonic balance principle , the period doubling bifurcation and chaos behaviors are discussed by theory , for the multidimensional magnetic levitation control system .

基于高维磁悬浮控制系统的倍周期分叉、混沌特性，从理论上提出了一种确定控制器参数范围的近似方法。

For fractional logistic delay system , in the bifurcation curve with respect to fractional order , when fractional order decreases , it shows a period doubling bifurcation to chaotic motion .

对于分数阶时滞系统，在分数阶阶次的分岔图中，当阶次逐渐减小时，出现分岔周期倍化走向混沌运动的现象。

For fixed damping and fixed excited frequency the motion of the beam under small amplitude of force is periodic , but becomes chaotic through period doubling bifurcation with increase of the force .

对固定的参数激励频率和阻尼，当参数激励幅值较小时梁的运动是周期的，但大幅值激励会使运动通过倍周期分岔变为混沌。

The Floquet theory is applied to study the stability and the bifurcation of periodic solution . It is found that periodic solution quasi periodic bifurcation , period doubling bifurcation occur with certain parameters .

本文采用Floquet理论对其周期解的稳定性进行了计算分析：随着系统参数的变化，该系统将出现稳态周期解、准周期分岔、倍周期分岔。

During the process that varying the frequence of the external exciting force , we observe the process of the system changing from the simple periodic motion to the period doubling bifurcation , then the transition route of bifurcation to chaos .

在改变外界强迫力频率的过程中，观察系统从简单的周期运动到周期倍化分岔道路，再从周期倍化分岔到混沌的过渡道路。

By continuation of periodic solutions , it is observed that the bifurcating periodic solutions , which emerge from Hopf bifurcation , lose their stability and period doubling bifurcation occurs when a delay goes beyond a certain value .

延拓分叉周期解，表明时滞超过临界值时，其周期解失去稳定性，出现了倍周期分叉。

The theory obtained herein is applicable not only to period doubling bifurcation and Hopf bifurcation of multi parameter vibro impact systems with two degree of freedom , but also to those of the other dynamic systems which can be described as four dimension mapping systems .

其理论结果可以应用于确定含多参数的两自由度碰撞振动系统的周期倍化分叉和Hopf分叉的分叉参数临界值。

The nonlinear dynamic equation of cavitation bubble radial motion has been investigated numerically after accounting for the liquid compressibility . It is shown that the bubble motion presents the intense feature of nonlinear dynamics and the period doubling bifurcation is one of the routes to chaos .

在考虑了液体可压缩性的影响后，对空泡径向运动的非线性动力学特性进行了数值研究，结果表明空泡运动呈现强烈的非线性动力学特性，倍周期分岔是空泡运动达到混沌的途径之一。

DC-DC switching power converter is a typical piecewise-smooth dynamical system . In this circuit system , all kinds of bifurcations such as the period doubling bifurcation , Hopf bifurcation , Border collision bifurcation and chaotic motion can be generated under some working and parameter conditions .

DC-DC开关功率变换器是一种典型的分段光滑动力学系统，在一定的工作和参数条件下，系统会出现各种分岔如倍周期分岔、Hopf分岔、边界碰撞分岔和混沌运动。

On the Period - Doubling Bifurcation of the Solutions of the First Order Exponential Logistic Iterative Equation

指数型一次Logistic迭代方程解的周期倍分岔现象

The sub harmonious , quasi period , chaotic motions and a cascade of period doubling bifurcation happens and then lead to chaotic motion is illustrated .

揭示了SFD转子系统在特定参数范围内存在系统亚谐波、概周期和混沌等非协调运动，及从同步周期运动分叉发生一系列倍周期运动、最后导致转子轴承系统混沌运动的过程。