period doubling bifurcation meaning in English
倍周期分岔
Examples
- The process from period doubling bifurcation to chaos suggests us to adjust the regulatory parameters in the system actively and scientifically , which will help the development of new system and lead the system ' s movement into the expected direction
由倍周期分岔通向混沌的道路启发人们主动地、科学地调节系统的控制参数，诱发新机制的形成，引导系统的运动朝着人们所期望的方向发展。 - The dynamics behaviors of the flexible jeffcott rotor system supported by unsteady short dynamic bearing are investigated . based on nonlinear unsteady - state dynamic n - oil film force model described by three functions the local stability of the periodic solutions with the controlling parameters , rotational speed ratio , imbalance amount , damping ratio and viscidity , are predicted by using the floquet multiplier . it is found that the period doubling bifurcation is caused by a certain imbalance amount and the hopf bifurcation is created by the lost stability of the oil - film
研究了非稳态动载短轴承支撑的jeffcott柔性转子系统的动力特性，基于可用三个函数表示动态油膜的非稳态非线性油膜力模型，将转速比、不平衡量、阻尼比、粘度作为控制参数，利用floquet乘子预测周期解的局部稳定性，发现倍周期分叉是由一定量的不平衡引起的，而hopf分叉是由油膜失稳造成的。 - In addition to the familiar period doubling bifurcation scenario leading to chaos , a quasiperiodic route to chaos is also observed which occurs through an initial hopf bifurcation . the current chaos control methods are compared , the stabilization of unstable periodic orbits of this chaotic system is achieved by continuous feedback control method , the specially designed external oscillator which used as target motion orbit in continuous feedback control method is obtained directly from ihb method
对现有的混沌控制方法的优缺点进行了比较，利用混沌控制理论中的连续变量反馈控制方法，实现了系统混沌吸引子内部的不稳定周期轨道的稳定化，对齿轮传动系统进行了有效的混沌控制，并对连续变量反馈方法的结果进行了分析，包括噪声的影响和方法的改进。 - The radiation field evolves from a steady saturation state to a limit cycle oscillation state , and eventually to chaotic oscillation state as the current increases , the region in which the field exhibits limit cycle or chaotic oscillation is called the " soft " and " hard " nonlinear regime , respectively : ( 1 ) in the " soft " nonlinear regime , the radiation field is characterized by period doubled bifurcation and the discrete power spectrum
随着电流的增大，辐射场经历由稳定饱和到极限环型的周期振荡，并最终过渡到非周期性混沌振荡的演化过程，按其状态可分为“软”和“硬”两种非线性区域： ( 1 )在“软”非线性区域，场的极限环振荡态和稳定饱和态是交替出现的，其特征是典型的倍周期分岔，输出功率谱是分立的。 - We , in chapter 4 , comprehensively discuss the dynamics of discrete chaotic neural networks , including f the existence of fixed points , the stable , unstable dynamics of the fixed point , the saddle - node and period doubling bifurcations in singie neuron model , and chaotic dynamics of the networks . the proofs and de - ductions involve schauder fixed point principle , constructions of lyapunov func - tions , bifurcation theory , contraction map principle , and anti - integrable limit method
在本文的第四章中，我们首先介绍了离散混饨神经元、神经网络模型由来与具体的数学模型，依次给出了该离散神经网络的中不动点存在性与惟一性的分析：稳定性与不稳定性的分析；神经元模型的分枝分析；神经网络中马罗陀意义下混3屯动力学的分析