Optical communication with synchronized hyperchaos generated electrooptically

We propose a method based on a scalar second-order difference-differential equation to obtain intensity chaos from a laser diode with a nonlinear delayed feedback. The method can be used for encrypting, transmitting, and decrypting a signal in a chaos-based communication system. The core of the chaotic transmitter and receiver is formed by an electrooptic modulator that is used to generate a strong reproducible nonlinearity and chaotic waveforms of extremely high Lyapunov dimensionality. The system opens the way to ultrafast chaotic communications.     

Inducing Chaos in Electronic Circuits by Resonant Perturbations

We propose a scheme to induce chaotic attractors in electronic circuits. The applications that we are interested in stipulate the following three constraints: 1) the circuit operates in a stable periodic regime far away from chaotic behavior; 2) no parameters or state variables of the circuit are directly accessible to adjustment and 3) the circuit equations are unknown and the only available information is a time series (or a signal) measured from the circuit. Under these conditions, a viable approach to chaos induction is to use external excitations such as a microwave signal, assuming that a proper coupling mechanism exists which allows the circuit to be perturbed by the excitation. The question we address in this paper is how to choose the waveform of the excitation to ensure that sustained chaos (chaotic attractor) can be generated in the circuit. We show that weak resonant perturbations with time-varying frequency and phase are generally able to drive the circuit into a hierarchy of nonlinear resonant states and eventually into chaos. We develop a theory to explain this phenomenon, provide numerical support, and demonstrate the feasibility of the method by laboratory experiments. In particular, our experimental system consists of a Duffing-type of nonlinear electronic oscillator driven by a phase-locked loop (PLL) circuit. The PLL can track the frequency and phase evolution of the target Duffing circuit and deliver resonant perturbations to generate robust chaotic attractors     

Chaos from second-order PLL in presence of CW interference

The chaotic behaviour of a second-order phase-locked loop (PLL) in the presence of continuous wave (CW) interference is examined. The Lyapunov exponents and dimension of the system are calculated to confirm the chaotic phenomenon. A range of interfering signal power and frequency has been found where chaos could occur     

Chaotic dynamics of delayed feedback klystron oscillator and its control by external signal

Complex nonlinear dynamics and applications of a microwave klystron oscillator with delayed feedback are studied in this paper on the basis of a system of delayed differential equations. Results of numerical simulation of self-modulation and chaotic regimes are presented, unveiling a complex bifurcation pattern in a wide range of parameters. Various types of chaotic attractors and transition to chaos scenarios are described. Experimental results for the five-cavity klystron oscillator are presented as well, showing good qualitative agreement with numerical simulations. Special attention is paid to application of the oscillator in direct chaotic communications. Information transmission using chaos shift keying (CSK) modulation and coherent reception is demonstrated via numerical simulation. The driving by an external signal is used to control the chaotic states of the transmitter oscillator for the purpose of generation of CSK basis functions.     

一类非线性系统的混沌反控制研究

针对一类非线性系统的混沌反控制问题,借用非线性状态观测器概念设计实现混沌反控制的控制器。非混沌系统在控制器的控制下,在与混沌系统的输出实现同步的同时,使非混沌系统处于混沌状态,实现混沌反控制的目标。理论分析及仿真结果都证明该方案的有效性和可行性。     

外光注入八字形腔的混沌动力学研究

基于外光注入带反馈的非线性光环镜理论模型,数值研究了外光注入八字形腔的混沌动力学特性。结果表明,随着外光注入功率的增加,非线性光纤环镜将经历倍周期进入混沌,这主要是由于注入的光信号在非线性环内传输的过程中由于光纤的非线性克尔效应产生非线性相移,光场经过多次迭代最终实现了混沌输出,为利用非线性光纤环镜实现混沌激光的输出提供了理论指导。     

Generation of multi-scroll delayed chaotic oscillator

A novel delayed chaotic oscillator capable of generating multi-scroll chaos is investigated. The nonlinear activation function can be represented as a piecewise linear function, and its circuitry implementation requires only a few operational amplifiers. The typical waveforms and phase portraits of the attractor are presented to illustrate mono-, two- or four-scroll chaotic oscillations     

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。     

Considerations of Nonlinear Effects in Phase-Modulation Systems

A class of "optimum" phase modulation (PM) system treated in the past is one wherein a sinusoidal carrier is phase modulated linearly by a Gaussian (baseband) random process and demodulation is performed by a phase-locked loop (PLL). This paper is concerned with PM systems in which the phase modulation is allowed to be nonlinear. In practice, most phase modulators are restricted to finite ranges of linear operations. The performance (SNR) of the PLL demodulator is degraded when the linear range is exceeded by an amplitude of the modulating waveform. The occurrence of performance degradation is a random event whose frequency depends on the linear range and the statistics of the waveform amplitude. By interpreting the nonlinear phase modulation as a saturation phenomenon, we determine in this paper the performances of PLL de modulator as a function of varying degree of saturation (or limiting) level for several cases of baseband spectrums. We model the "saturation" by an error function limiter. Our results are general, and it is shown that the previous results of linear modulations are special cases of our results. We then move on to assume that the baseband waveform is a composite signal of multichannel frequency division multiplexed (FDM) signals. As a result, we compute the lower bounds of slgnal-to-crosstalk power ratio for several cases of baseband spectrums.     

应用锁相环技术判别混沌相变的方法

针对经典的李氏指数法(Lyapunov Exponential Method)等混沌相变判别方法复杂度高的问题,提出了一种应用锁相环技术判别混沌相变的新方法.首先,理论推导了混沌系统的解析特性,分析了系统在不同相态下含有的频率成分;然后,构建了针对混沌系统的数字锁相环模型,研究锁相环下混沌态和大周期态呈现的频率特性;最后,提出了一种基于锁相环技术的混沌相变判别新方法.仿真实验显示,相比于李氏指数法,所提方法判别速度快一个数量级,检测差错率为0时,性能提高近2 dB.新方法应用锁相环技术,简便易行,判别速度快,为混沌相变判别的工程应用提供了新的手段.     

一种新型非线性PLL模型及其在毫米波集成防撞雷达中的应用

提出了一种新的非线性PLL用于VCO的非线性补偿,利用声表面波延迟线来实现延时混频,并将混频后的中频信号锁定PLL结构,深入分析了这种PLL的环路相位模型,使用Agilent ADS软件对锁相环路进行了仿真,验证了所提出的环路相位模型的准确性,所有的理论推导和仿真结果表明,建立的PLL环路相位模型可以用来实现防撞雷达中VCO(电压控制振荡器)的线性化,准确可靠,利于雷达系统的集成化和高精度。     

Stabilizing periodic solutions of nonlinear systems and applications in chaos control

In this paper, a simple nonlinear recursive delayed feedback controller is designed for stabilizing periodic solutions of a nonlinear system. The proposed controller is constructively designed and does not inherit the odd number limitation. The stability of the periodic solution of the closed-loop system is proved rigorously. Applying the control method to chaotic systems, one can effectively control chaos.     

混沌理论在测量中的应用

提出了一种在极不稳定的混沌系统中进行信号测量的方法，将敏感元件作为混沌电路的一部分，在初值一定的条件下，利用混沌系统的参数敏感性，敏感元件的参数随待测信号变化并使系统的混沌轨道变化，定义了轨道距离。从理论上和特定电路实验上论证了混沌测量方法是可行的。     

自组织反馈光纤环形激光器相位调制产生强度混沌的实验研究

报道了自组织反馈光纤环形激光器中施加相位调制后产生的强度混沌现象。对自组织反馈光纤环形激光器进行稍大于阈值的泵浦,通过压电陶瓷引入相位调制;保持泵浦功率及调制电压不变,改变调制频率,得出光强随不同调制频率变化的分岔图,观察到某些特定频率区域内激光器输出进入类似混沌的状态。针对类似混沌的光强输出序列进行非线性时间序列分析,通过功率谱计算、相空间重构、关联积分计算等方法得到了多段调制频率区间内光强序列具有混沌特征的证据。初步分析产生混沌的机理得出:特定条件下施加的相位调制等同于损耗调制。     

混沌信号在色散光纤传输过程中的演化

研究了色散光纤混沌传输理论及混沌信号与色散光纤相互作用的物理机制;通过耦合激光混沌系统和色散光纤传输信道,提出了色散光纤混沌信号传输演化物理模型;提出混沌信号在色散光纤传输中的非线性演化频率啁啾和公式;着重分析光纤色散对激光混沌信号传输与演化的作用,色散能够展宽混沌信号脉冲,但不影响混沌信号的形状;色散能够改变混沌信号每个频谱分量相位,但不影响混沌信号频谱形状;色散能够改变混沌信号光场慢变场分量的变化,但不改变混沌信号包络时变特性,也不影响混沌信号脉冲的功率分布和场强分布;色散能够改变混沌吸引子在相空间整体旋转角度并使其旋转角度随光纤传输长度而发生改变,但不改变混沌吸引子在相空间中的内部结构.最后数值模拟了混沌信号在光纤传输过程中的相位、场慢变部分分量以及混沌吸引子等演化形式等.     

Chaotic electronic oscillator from single amplifier biquad

The present letter reports a simple chaotic electronic oscillator. A single amplifier biquad (SAB) based active high-Q Band Pass Filter (BPF) is converted into a chaotic oscillator by introducing a single passive nonlinear element in the form of a general purpose pn junction diode, and a storage element in the form of an inductor. The chaotic circuit is mathematically modeled, which is a set of four coupled first-order autonomous nonlinear differential equations. The behavior of the proposed circuit is investigated through numerical simulations and electronic hardware experiments. It is found that the circuit shows complex behaviors, like, bifurcations and chaos, for a certain range of circuit parameters. The chaotic behavior of the circuit is ensured qualitatively by bifurcation diagram, phase plane plot and experimentally obtained power spectrum, and quantitatively by Lyapunov exponents and Kaplan–York dimensions.     

Using modern RF tools to detect chaotic behaviour of electronic circuits and systems

In this paper, a new approach in identifying chaotic behaviour of nonlinear circuits is presented. This approach could be very useful to circuit designers, whether they pursue a chaotic behaviour or not. Simulation tools used for radio-frequency circuit design (Cadence SpectreRF), initially developed to characterise harmonic oscillators, are now utilised to detect chaotic behaviour, as well as routes to chaotic mode of operation. Specifically, Periodic Steady State Convergence Norm is used for the first time for chaos detection in circuits. The advantages of this method (especially in terms of simulation time) are presented, together with an example of detection of chaotic route to chaos in the case of a chaotic-operating Colpitts oscillator.     

用变量旋转变换实现声光双稳系统的混沌控制

设计了一种控制非线性系统混沌的变量旋转变换(VRT)方法。介绍了变量旋转变换方法的控制原理,并用此方法控制声光双稳(AOB)系统的混沌,以此验证其有效性。利用计算机仿真模拟了受控后声光双稳系统的动力学行为。模拟结果显示,旋转变换的关联系数cosθ,sinθ为系统的控制参数,通过恰当地选择旋转变换的关联系数,使受控后系统的李雅普诺夫(Lyapunov)指数λ由正值转变为负值,系统由混沌态转变为周期态,周期态不但有稳定的原系统存在的倍周期2np轨道,而且还有3mp,2n×3mp(n,m为整数)这样原系统以外的周期轨道。     

基于余幂-激活离散超混沌加密的多参数加权分数傅里叶变换安全通信方法

为提高物理层安全传输性能,该文提出一种新的基于2维余幂-激活(2D-CPA)离散超混沌加密的多参数加权分数傅里叶变换(MP-WFRFT)安全通信方法。首先,将激活函数和余弦函数作为非线性因子引入1维立方(cubic)混沌映射,构造2维混沌映射。非线性因子可对原始cubic混沌映射的迭代过程进行扰动,从而获得更加饱满的相轨。利用分岔图、相图、Lyapunov指数谱等对提出的2维混沌映射动力学特性进行了验证。结果表明,构造的2维混沌序列随机性良好,可进入超混沌状态。然后,利用余幂-激活离散超混沌序列分别构建幅度变换矩阵、相位旋转矩阵和MP-WFRFT参数池,完成对星座幅相加密,以及MP-WFRFT动态变换加密过程,进一步消除数据统计特征,同时提升MP-WFRFT变换的抗参数扫描性能。数值仿真结果表明,加密数据的星座图呈类高斯分布,且传输系统对密钥的敏感性良好。     

A hybrid chaotic map for communication security applications

Recently, the synchronization between two matching chaotic systems to provide confident communication has gained a lot of interest. Continuously, there is a necessity to produce a novel dynamical system to be used in synchronization to implement a strong security system. In this paper, a hybrid chaotic system is suggested and verified for the potential use of secure communication through chaos synchronization. The Lyapunov exponent (LE) and zero‐one (0‐1) tests have been used to verify the performance of the suggested hybrid chaotic system, while National Institute of Standard and Technology (NIST) tests have been applied to verify the randomness properties. And the synchronization has been achieved between master and slave systems by using nonlinear control laws. The simulation outcomes demonstration that the hybrid system has chaotic performance and outstanding randomness characteristic. The statistical results gained for LE test was 0.8822, and for frequency test (FT) was 0.2028, while for the run test (RT) was 0.1924. Accordingly, the suggested hybrid system can be used to evolve functional synchronization algorithms and encryption for image, video, and voice secure communication applications.