Controlling Chaos in Hénon Map by the Constant Feedback Method

We demonstrate the constant feedback and the modified constant feedback method to the Hénon map. Using the convergence of the chaotic orbit in finite time, we can control the system from chaos to the stable fixed point, and even to the stable period-2 orbit or higher periodic orbit by the action of a proper feedback strength and pulse interval. We also find that the multi-steady solutions appear with the same control strength and different initial conditions. The aim of this control method is explicit and the feedback strength is easy to determine. The method is robust under the presence of weak external noise.     

相干长度可连续调谐的半导体激光器

实验利用光反馈的方法获得了相干长度连续可调的半导体激光光源.通过调节反馈强度及抽运电流,有效控制了光反馈半导体激光器的相干长度.其相干长度可由无反馈时的几米连续调至100 μm.同时,利用光反馈半导体激光器速率方程,数值模拟了反馈强度及抽运电流对半导体激光器相干长度的影响.实验及数值模拟均表明：通过调节反馈强度的大小可以有效控制半导体激光器的相干长度,光反馈半导体激光器的相干长度随反馈强度的增大而减小,而偏置电流对相干长度无明显影响.模拟结果与实验结果符合. 关键词： 光反馈半导体激光器 相干长度 反馈 混沌     

直接调制光反馈半导体激光器产生超宽带信号

利用直接电流调制光反馈半导体激光器产生了符合美国联邦通信委员会关于室内无线通信频谱限定的超宽带(UWB)微波信号.基于光反馈半导体激光器速率方程组, 数值分析了偏置电流、反馈强度对混沌UWB脉冲信号的影响.研究表明, 混沌UWB脉冲频谱的-10 dB带宽分别随着偏置电流的增大和反馈强度的增强而逐渐增加; 中心频率分别随着偏置电流的增大和反馈强度的增强而逐渐增大.实验中, 产生了中心频率为6.6 GHz, -10 dB带宽为9.6 GHz的混沌UWB信号. 进一步, 通过调节偏置电流和反馈强度, 可实现混沌UWB信号的中心频率和-10 dB带宽的可调谐输出, 实验结果和数值分析相符合.此外, 实验产生的混沌UWB信号经过34.08 km的光纤传输后, 其频谱形状几乎没有发生变化, 表明该方法所产生的混沌UWB信号对光纤色散有较大的容忍度. 关键词： 超宽带 混沌激光 光反馈 直接调制     

Markov Quantum Feedback Control Based on Homodyne Measurement of a Two-Qubit System

We consider the system consisting of two qubits collectively damped,with the output being unit-efficiency measured and subsequently fedback to control the system state. Our primary goal in this paper is (i) to solve the feedback-modified master equation, (ii) to demonstrate the ability of feedback control based on the solutions, and (iii) to pick out different steady states by choosing different driving strengths and feedback strengths tocounteract the effects of both damping and the measurement back-action on the system. We further investigate some properties of the equilibrium steady state, its distribution probability and entanglement vs. the driving and feedback amplitudes. We find that in our feedback model feedback plays a negative role in producing entanglement.     

调频微片Nd:YAG激光器光回馈特性的研究

研究了调频微片Nd：YAG激光器的光回馈特性.在没有光回馈的情况下，激光频率每改变一个纵模间隔，激光器输出功率变化一个条纹.有光回馈时，同时改变激光频率和外腔相位，激光器输出功率波动频率正比于内、外腔长度之比.基于三镜腔等效模型的理论分析和实验结果相符合.并且讨论了这一现象在精密测量领域的潜在应用.     

Dynamics of Semiconductor Lasers with Optical Feedback from Photorefractive Phase Conjugate Mirror

The dynamics of semiconductor lasers with photorefractive phase conjugate optical feedback are experimentally studied. Photorefractive fringes considered here are rather static compared with time fluctuations of laser output power. Therefore, it is expected that a semiconductor laser with photorefractive feedback shows similar dynamics to those with conventional optical feedback. We examine relaxation oscillation and external cavity modes of laser output power in the presence of photorefractive phase conjugate feedback. It is proved that the dynamics of photorefractive phase conjugate feedback are fundamentally the same as those of conventional optical feedback.     

Control of coexisting attractors via temporal feedback

We propose a method for controlling coexisting attractors in multistable dynamical systems. In this method, the feedback for an initial duration of time can drive the system to the desired state. We have illustrated this method by considering temporal feedback in autonomous as well as non-autonomous dynamical systems. The experimental realisation of the proposed method is also presented.     

Cascading failures in congested complex networks with feedback

In this article, we investigate cascading failures in complex networks by introducing a feedback. To characterize the effect of the feedback, we define a procedure that involves a self-organization of trip distribution during the process of cascading failures. For this purpose, user equilibrium with variable demand is used as an alternative way to determine the traffic flow pattern throughout the network. Under the attack, cost function dynamics are introduced to discuss edge overload in complex networks, where each edge is assigned a finite capacity (controlled by parameter α). We find that scale-free networks without considering the effect of the feedback are expected to be very sensitive to α as compared with random networks, while this situation is largely improved after introducing the feedback.     

Feedback control strategies for the Liu chaotic system

This Letter proposed three strategies of the dislocated feedback control, enhancing feedback control and speed feedback control of the Liu chaotic system to its unstable equilibrium points. It is found that the coefficients of enhancing feedback control and speed feedback control are smaller than those of ordinary feedback control, so, the complexity and cost of the system control are reduced. Theoretical analysis and numerical simulation are given, revealing the effectiveness of these strategies.     

基于非准直外腔的单频激光高阶回馈效应研究

对基于非准直外腔的单频激光高阶回馈现象及产生机理进行了研究,获得了调制幅度不均匀的高分辨率多重高阶回馈条纹,分析了多重高阶回馈条纹的特点及产生机制。提出采用基于光路阻挡的实验方法,在回馈镜反射率大于90%的强回馈中,发现了单重高阶回馈效应,获得了调制幅度均匀、无大包络的高分辨率单重高阶回馈条纹,其分辨率达到/10,而且还有进一步提高的潜力。单重高阶回馈条纹不但具有多重高阶回馈时高分辨率的优点,还具有传统弱回馈时调制幅度均匀、类正弦等特性,对进一步研制高精度回馈测量系统具有重要意义。     

半导体激光器输出混沌光的延时特性和带宽

提出一个新的方案用于抑制半导体激光器输出混沌光的延时特性并研究其带宽.在该方案中,将由伪随机信号驱动的相位调制器加到具有双路光反馈的半导体激光器的两个反馈腔中,从而构成具有双路相位调制光反馈的分布反馈半导体激光器系统.数值研究了延迟时间和反馈系数等参数对该系统输出混沌光的延时特性的影响,用自相关函数曲线中的延时特征峰的最大值表示延时特性.然后将该系统对延时特性的抑制效果和具有双路光反馈的分布反馈半导体激光器系统以及具有单路相位调制光反馈的分布反馈半导体激光器系统进行比较,结果表明本文所提出方案的抑制效果最好.进而基于能有效抑制延时特性的参数条件研究了具有双路相位调制光反馈的分布反馈半导体激光器输出混沌光的带宽,结果表明,抽运因子的增大和反馈系数的增加都能使系统输出混沌光的带宽变大.     

反馈强度对外腔反馈半导体激光器混沌熵源生成的随机数序列性能的影响

外腔反馈半导体激光器在合适的反馈强度下将呈现混沌态, 其输出的激光混沌信号可作为物理熵源获取物理随机数序列. 着重研究了外腔反馈强度对最后获取的二元码序列的随机性的影响. 数值仿真结果表明, 随着反馈强度的增加, 外腔反馈半导体激光器输出的混沌信号的延时时间特征峰值呈现先逐渐减小再逐渐增大的过程, 而对应的排列熵特征值呈现先增大、后缓慢降低的过程, 即存在一个优化的反馈强度可使输出的混沌信号的延时特征得到有效抑制且复杂度高. 利用NIST Special Publication 800-22软件对基于不同反馈强度下外腔半导体激光器输出的混沌信号所产生的二元码序列的随机性进行了相关测试, 并讨论了反馈强度的大小对测试结果的影响.     

A Suitable Active Control for Suppression the Vibrations of a Cantilever Beam

In our consideration, a comparison between four different types of controllers for suppression the vibrations of the cantilever beam excited by an external force is carried out. Those four types are the linear velocity feedback control, the cubic velocity feedback control, the non-linear saturation controller (NSC) and the positive position feedback (PPF) controller. The suitable type is the PPF controller for suppression the vibrations of the cantilever beam. The approximate solution obtained up to the first approximation by using the multiple scale method. The PPF controller effectiveness is studied on the system. We used frequency-response equations to investigate the stability of a cantilever beam. We notified that, there is a good agreement between the analytical solution and the numerical solution.     

Anharmonic resonances with recursive delay feedback

We consider application of time-delayed feedback with infinite recursion for control of anharmonic (nonlinear) oscillators subject to noise. In contrast to the case of a single delay feedback, recursive delay feedback exhibits resonances between feedback and nonlinear harmonics, leading to a resonantly strong or weak oscillation coherence even for a small anharmonicity. Remarkably, these small-anharmonicity induced resonances can be stronger than the harmonic ones. Analytical results are confirmed numerically for van der Pol and van der Pol-Duffing oscillators.     

耗散环境下三原子之间稳定纠缠的量子反馈控制

研究利用基于量子跳跃的量子反馈控制来产生三个二能级原子之间稳定的纠缠.考虑三个二能级原子处于一个严重耗散的单模光腔中,分别讨论了反馈作用在一个原子上和反馈同时作用在三个原子上的情况.研究发现:当反馈作用在某个原子上时,基于量子跳跃的量子反馈能够保护另外两个原子的最大纠缠态.当反馈同时作用在三个原子上时,选择合适的参数可以得到两个基矢张开的无消相干子空间,并且利用量子轨迹蒙特卡罗波函数方法,得到一定初始条件下系统最终可以演化到这个子空间中三个原子之间的最大纠缠态.     

Position and Velocity Time Delay for Suppression Vibrations of a Hybrid Rayleigh-Van der Pol-Duffing Oscillator

In this paper, we used time delay feedback to minimize the vibrations of a hybrid Rayleigh–van der Pol–Duffing oscillator. This system is a one-degree-offreedom containing the cubic and fifth nonlinear terms and an external force. We applied the multiple scales method to get the solution from first approximation. Graphically and numerically, we studied the system before and after adding time delay feedback at the primary resonance case (Ω ≌ ω). We used MATLAB program to simulate the efficacy of different parameters and the time delay on the main system.     

基于光线追迹的单频激光多重回馈效应研究

提出一种基于非准直平凹回馈腔的单频激光多重回馈光线追迹模型,采用该模型阐明了单频激光多重回馈效应的产生机理,分析了多重回馈高分辨率条纹的特性,明确了影响多重回馈条纹形状的主要因素,包括回馈镜的倾角、曲率半径、反射率以及回馈外腔长等,获得了回馈镜在不同倾角时的有效回馈阶次及其耦合系数。光线追迹分析与实验结果表明:当回馈镜倾斜角为1.7时,多重回馈效应会产生调制幅度均匀、没有大包络的高分辨率回馈条纹,每个条纹的分辨率可达/50。     

存在外部光反馈的半导体激光器的相位噪声

本文在理论上研究了由于外部光反馈引起的半导体激光器的相位噪声.理论分析是通过引入一个反馈耦合率K和线性化速率方程,导出了半导体激光器相位噪声功率谱密度的表达式.这表明相位噪声功率谱密度随外腔长度而周期性地漂移,且功率谱密度的峰值随外部反馈耦合率而发生很大的变化.     

Chaos dynamics in vertical-cavity surface-emitting semiconductor lasers with polarization-selected optical feedback

We study experimentally and numerically the dynamic states of chaotic oscillations in vertical-cavity surface-emitting semiconductor lasers (VCSELs) with polarization-selected optical feedback. We identify the regimes of fully-developed chaotic states, low-frequency fluctuations (LFFs), and coexistent states of LFFs and stable oscillation for the variations of the bias injection current and the optical feedback ratio. In particular, coexistent states of LFFs and stable oscillations are observed at higher optical feedback ratio and lower bias injection current. We draw maps of dynamic states in the space of the bias injection current and the optical feedback ratio. The qualitative agreement between the theory and the experiment is found.     

外反馈He—Ne激光器的非稳特性研究

报道了平面镜和自泵浦相位共轭镜反馈Ｈｅ－Ｎｅ激光器的非稳特性，观测了反馈镜位置对激光光强起伏及波动频率的影响，即在半腔长的整数倍附近，激光光强具有较大的起伏和秒量级的准周期振荡，并对其产生机理进行了分析。