Chaos Controlled ZCDPLL for Carrier Recovery in Noisy Channels

The objective of this work is to analyze the performance of the chaos controlled first order Zero Crossing Digital Phase Locked Loop (ZCDPLL) in the presence of Additive White Gaussian Noise (AWGN). The nonlinear behaviour of ZCDPLL shows a period doubling to its route to chaos. The amount of ZCDPLL divergency is measured and fed-back in a form of linear stabilization. The introduction of the chaos control widens the lock range of a ZCDPLL and improves the loop’s operation in the presence of AWGN.     

电流激励蔡氏电路混沌的解析预测

考虑到蔡氏电路受周围电路的影响,故将受周围影响的蔡氏电路做了等效处理,并将其等效为电流激励蔡氏电路。这里首次用解析的方法对三阶非线性微分方程能够产生混沌的参数范围进行预测,利用该方法得出电流激励蔡氏电路产生混沌的必要参数条件。通过数值仿真证明了该等效电路具有极其丰富的混沌动力学行为,仿真结果与解析预测结果有较好的吻合性。     

Chaotic generation based on figure-of-eight erbium-doped fiber laser with an optical fiber ring

We experimentally demonstrate the chaotic generation in a figure-of-eight erbium-doped fiber laser (F8L) with an optical fiber ring (OFR). With an appropriate combination of polarization controllers, we find that the fiber laser exhibits period-doubling route to chaos, and the chaotic self-synchronous dynamics has a tendency to be reduced significantly. The experimental results show the tendency is related to the interference and the nonlinear phase shift of light in the optical fiber ring. Meanwhile, the chaotic dynamics is related to the polarization state and pump power.     

Chaotic pulsing and quasi-periodic route to chaos in asemiconductor laser with delayed opto-electronic feedback

Chaotic pulsing and the route to chaos in a semiconductor laser with delayed, positive opto-electronic feedback are investigated numerically and experimentally. Both numerical simulation and experimental observation indicate that the laser enters a chaotic pulsing state at certain delay times of the feedback loop through a quasi-periodic route. The characteristics of each dynamical state are analyzed. The chaotic pulsing state is verified with a positive Lyapunov exponent and a fractal correlation dimension. The experimental results show very good qualitative agreement with the numerical results. Quantitative discrepancy between experimental and numerical results can be explained by the bandpass characteristics of the electronic feedback loop     

Simulation studies of frequency locking, quasi-periodicity,subharmonic bifurcation, and chaos in modulated semiconductorlasers

A method of finding self-consistent solutions for the field equation and rate equations has been used to study frequency locking, quasi-periodicity, subharmonic bifurcations, and chaos in gain-guided stripe-geometry semiconductor lasers under high-frequency modulation current. The results show that chaotic behavior arises in unstable semiconductor lasers. The route to chaos is not through period doubling, but rather through quasi-periodicity. The frequency-locked regions have been studied. For lasers whose dynamic response exhibits quickly damped relaxation oscillations, only period-two oscillations have been obtained. The calculated results agree with experiment     

Chaos in semiconductor lasers with optical feedback: theory andexperiment

The authors present a detailed theoretical and experimental investigation of the nonlinear dynamics of a semiconductor laser with optical feedback. The results show that the coherence collapsed state is a chaotic attractor and that chaos is reached for increasing feedback level through a quasi-periodic route interrupted by frequency locking. Furthermore, the coexistence of two attractors, associated with the same external cavity mode, but having different relaxation oscillation frequencies, is demonstrated and explained     

FIR digital filter-based ZCDPLL for carrier recovery

The objective of this work is to analyse the performance of the newly proposed two-tap FIR digital filter-based first-order zero-crossing digital phase-locked loop (ZCDPLL) in the absence or presence of additive white Gaussian noise (AWGN). The introduction of the two-tap FIR digital filter widens the lock range of a ZCDPLL and improves the loop’s operation in the presence of AWGN. The FIR digital filter tap coefficients affect the loop convergence behaviour and appropriate selection of those gains should be taken into consideration. The new proposed loop has wider locking range and faster acquisition time and reduces the phase error variations in the presence of noise.     

Third-order RLCM-four-elements-based chaotic circuit and its coexisting bubbles

This paper presents a new third-order RLCM-four-elements-based chaotic circuit, in which the memristor element is equivalently implemented by a diode-bridge cascaded with an inductor. Mathematical model is established and its equilibrium stability is analyzed. The dynamical properties of the memristive chaotic circuit are disposed by MATLAB numerical simulations and confirmed by breadboard experimental measurements. In particular, the antimonotonicity phenomena of coexisting periodic and chaotic bubbles are observed under some specified control system parameters and the evolutions of coexisting bubbles are exhibited with the variations of two control system parameters. The presented memristive chaotic circuit is very simple and only third-order but can emerge complex dynamics with chaos, period, coexisting bifurcation modes, and coexisting bubbles.     

混沌信号与噪声

本文通过三种方法分别研究了Lorenz模型和高斯白噪声，获得了混沌信号和噪声在这些方法下的不同表现特征。提出了根据关联维数（correlationdimension）判断降噪效果的方法，并进一步探讨了采用主分量分析（principalcomponentanalysis）确定嵌入维数（embeddingdimension）和去除混沌信号中噪声的可行性。最后得出结论：主分量分析用于确定嵌入维数和降低混沌信号中的噪声是不合适的。     

Comparison of the effects of nonlinear gain and weak opticalfeedback on the dynamics of semiconductor lasers

The influence of nonlinear gain and optical feedback on the dynamics of single-mode semiconductor lasers are numerically investigated based on the Lang and Kobayashi model. It is well known that the nonlinear gain tends to stabilize the dynamics, while the optical feedback tends to increase the instabilities. In this paper, we study the behavior of the attractors when the feedback level k and the gain saturation coefficient ε vary and show that the effects of these parameters are surprisingly opposite. For example, we find that the route to chaos that the external cavity modes follow for increasing k is reversed for increasing ε in an almost identical manner. When the feedback increases the modes follow the usual quasi-periodic route and turn into torus. If k continues to increase, the torus become chaotic attractors as the result of several period-doubling bifurcations or a third Hopf bifurcation. Further increase of k causes the chaotic attractors to lose stability, Contrarily, if the value of the parameter ε is increased, the attractors recover their stability and reverse the route becoming simple torus again. If ε is increased further, the torus reverse the quasi-periodic route and turn into stable modes again. We also find that on the contrary to k, the parameter ε enhances the stability region of an attractor. We show that the feedback level above which a limit cycle emerges from a stable mode, the feedback level above which a torus emerges from a limit cycle, and the feedback level above which a chaotic attractor loses stability are all increasing functions of ε     

Period tripling and chaos in the dynamic behavior of directlymodulated diode lasers

The paper presents the relevance of period-tripling behavior that has recently been found in different experimental studies of directly modulated laser diodes. Applying different numerical techniques to the rate equation model of the laser diode, among which we highlight the continuation method to calculate the unstable solutions of the system, we show that period-tripling behavior appears and disappears in two tangent bifurcations. Therefore, the period-three solutions form a closed bifurcation curve called isola. In between these two tangent bifurcations, the period-three solution coexists with the chaotic attractor reached by a period-doubling cascade, giving rise to a hysteresis loop in the deterministic case. Also, we have found that a boundary crisis might be behind the chaotic behavior that is observed for the highest values of the modulation index. The effects of random noise fluctuations in the laser diode dynamics are also studied. Langevin noise sources are included in the rate equation model and appropriate stochastic integration methods have been used. The route to chaos that we have obtained points out the relevant role that noise has in achieving agreement between numerical studies and experimental results that have been published. The introduction of noise has been proved to be of major importance in determining the system behavior in the regions of the coexistence of solutions     

A novel current-controlled memristor-based chaotic circuit

In this paper, a novel third-order autonomous memristor-based chaotic circuit is proposed. The circuit has simple topology and contains only four elements including one linear negative impedance converter-based resistor, one linear capacitor, one linear inductor, and one nonlinear current-controlled memristor. Firstly, the voltage-current characteristic analysis of the memristor emulator for different driving amplitudes and frequencies are presented. With dimensionless system, the symmetry, equilibrium point and its stability are analysed. It is shown that the system has two unstable saddle-foci and one unstable saddle. A set of typical parameters are chosen for the generation of chaotic attractor. Differing from the common period-doubling bifurcation route in smooth dynamical systems, this memristive system shows abrupt transition from the coexisting period-1 limit cycles to robust chaos when varying system parameters. Various dynamical behaviors are analysed using the numerical simulations and circuit verifications.     

单反馈He-Ne激光器混沌激光产生的理论及实验研究

基于外光反馈机制,利用He-Ne激光器(中心波长为632.8nm)进行了混沌激光产生的理论及实验研究。在固定抽运电流和外腔长度的情况下,研究不同反馈系数对He-Ne激光器输出特性的影响。理论及实验结果表明:He-Ne激光器在单反馈下随着反馈系数的增大可通过周期态进入混沌。     

视觉注意驱动的基于混沌分析的运动检测方法

提出了视觉注意驱动的基于混沌分析的运动检测方法(MDSA)。MDSA首先基于视觉注意机制提取图像的显著区域,而后对显著区域进行混沌分析以检测运动目标。算法技术路线为:首先根据场景图像提取多种视觉敏感的底层图像特征;然后根据特征综合理论将这些特征融合起来得到一幅反映场景图像中各个位置视觉显著性的显著图;而后对显著性水平最高的图像位置所在的显著区域运用混沌分析的方法进行运动检测;根据邻近优先和返回抑制原则提取下一最显著区域并进行运动检测,直至遍历所有的显著区域。本文对传统的显著区域提取方法进行了改进以减少计算量:以邻域标准差代替center-surround算子评估图像各位置的局部显著度,采用显著点聚类的方法代替尺度显著性准则提取显著区域;混沌分析首先判断各显著区域的联合直方图（JH）是否呈现混沌特征,而后依据分维数以一固定阈值对存在混沌的JH中各散点进行分类,最后将分类结果对应到显著区域从而实现运动分割。MDSA具有较好的运动分割效果和抗噪性能,对比实验和算法开销分析证明MDSA优于基于马塞克的运动检测方法（MDM）。      

平均电流控制型PFC Boost变换器中的低频分岔现象研究

在设计和分析平均电流控制型功率因数校正(PFC)Boost变换器时,通常假设其工作在电流连续模式下,而采用电流连续模式下的平均模型分析变换器的动力学特性.而实际的变换器可能工作在电流断续状态,当变换器负载较小时,电流断续状态更加明显.因此,采用电流连续状态下的平均模型无法准确描述变换器的特性,尤其是混沌和分岔现象.本文采用考虑电流断续工作状态的状态空间模型,对PFC变换器中的低频分岔现象进行了分析,得到了低频分岔图,使该变换器由倍周期分岔到达混沌的路径更加清楚,使人们可以更全面理解这种变换器的动力学行为.并从分岔的角度分析了变换器的稳定性.其结果表明,变换器的输出电容和负载对变换器的稳定性具有很强的影响.通过给出的参数分岔图和二维参数与稳定性的映射图,为更好地设计变换器提供了指导.仿真分析结果和实验结果表明了本文所提方法的合理性和结果正确性.     

一种新的基于混沌的语音、噪声判别方法

语音通信中,区别发音段和非发音段具有一定的意义。其关键在于提取发音段和非发音段的不同特征参数。本文基于混沌信号处理,提出了一种新的语音、噪声判别方法。该方法提取信号在不同相空间重构维下的虚邻点,从而根据信号高维虚邻点平台的不同,判别发音段和非发音段（背景噪声）以及发音段所含噪声的强弱,本文阐述了该方法的原理,讨论了其性能,仿真实验表明,本方法具有较好的结果。     

耦合混沌系统时空动力学的模拟研究

研究了相同结构的混沌系统耦合后所得到的新系统的时空动力学行为及其系统特性.通过计算机仿真得到了耦合系统的分岔图和Lyapunov指数;在系统初值受噪声干扰的情况下,对混沌轨道偏移的均方根误差值与参与耦合的混沌子系统数量之间的关系进行了研究.计算机仿真结果证明,耦合后得到的新系统仍然是混沌态的,因此,它依旧保持了对初值的敏感性;但同时降低了混沌轨道指数漂移的不稳定性,在一定程度上抑制了噪声对系统初值的干扰.     

三阶非自治电路中的混沌振荡

本文研究在正弦电源激励下的三阶电路中的非线性动力性质。在该电路中，唯一的非线性元件是分段线性的负电阻元件。计算机模拟和电路实验表明，该电路在电源电压的有效值改变时，振荡制式会有如下之演变：周期—拟周期—混沌—亚超混沌—混沌—周期。此处所谓的亚超混沌振荡，是指相空间轨线的吸引子具有( ，0，0，-)类型的李雅普诺夫指数谱的振荡制式而言的。这种亚超混沌振荡制式在现有的非线性电路与系统的文献中尚不曾有过报道。本文的计算机模拟结果与电路实验结果之间有较好的吻合。     

Detection of signals in chaos

In this paper, we present a new method for the detection of signals in “noise”, which is based on the premise that the “noise” is chaotic with at least one positive Lyapunov exponent. The method is naturally rooted in nonlinear dynamical systems and relies on neural networks for its implementation. We first present an introductory review of chaos. The subject matter selected for this part of the paper is written with emphasis on experimental studies of chaos using a time series. Specifically, we discuss the issues involved in the reconstruction of chaotic dynamics, attractor dimensions, and Lyapunov exponents. We describe procedures for the estimation of the correlation dimension and the largest Lyapunov exponent. The need for an adequate data length is stressed. In the second part of the paper we apply the chaos-based method to a difficult task: the radar detection of a small target in sea clutter     

取样鉴相数字合成器环中的混沌动力学行为

分析和研究取样鉴相数字合成器环中的混沌动力学行为,根据Ushio与Hira等人的方法,从理论上证明了当系统参数满足一定条件时,系统会出现分岔现象,并具体计算出系统在各个不动点处的Hopf分岔集、系统的李雅普诺夫指数以及豪斯道夫维数。通过对系统进行计算机模拟,观察到系统的奇异吸引子,奇异吸引子的自相似性,系统在混沌状态下对初始条件的灵敏依赖性,进一步证实了三角形取样鉴相数字合成器环中存在混沌现象。