A novel chaotic system with one source and two saddle-foci in Hopfield neural networks

This paper presents the finding of a novel chaotic system with one source and two saddle-foci in a simple three-dimensional (3D) autonomous continuous time Hopfield neural network. In particular, the system with one source and two saddle-foci has a chaotic attractor and a periodic attractor with different initial points, which has rarely been reported in 3D autonomous systems. The complex dynamical behaviours of the system are further investigated by means of a Lyapunov exponent spectrum, phase portraits and bifurcation analysis. By virtue of a result of horseshoe theory in dynamical systems, this paper presents rigorous computer-assisted verifications for the existence of a horseshoe in the system for a certain parameter.     

Frequency locking,quasiperiodicity,and chaos in dual-frequency loss-modulated erbium-doped fiber lasers

Dynamic behaviors of the erbium-doped fiber laser （EDFL） with dual-frequency loss modulation are experimentally investigated. Frequency-locked states with their winding numbers which form the devil＇s staircase are observed in this kind of lasers. In the unlocked regions, the output state changes from quasiperiodicity to chaos under increasing modulation index, which demonstrates a different route to chaos from the conventional loss-modulated EDFLs with a single modulation frequency. The chaos output in the dual-frequency loss-modulated EDFLs shows less harmonic components of the modulation frequency in the corresponding power spectrum, indicating the improvement of the randomness of the chaotic signals.     

Study of dual-directional high rate secure communication systems using chaotic multiple-quantum-well lasers

A scheme of synchronized injection multi-quantum-well （MQW） laser system using optical couphng-feedback is presented for performing chaotic dual-directional secure communication. The performance characterization of chaos masking is investigated theoretically, the equation of synchronization demodulation is deduced and its root is also given. Chaos masking encoding with a rate of 5 Gbit/s and a modulation frequency of 1 GHz, chaos modulation with a rate of 0.2 Gbit/s and a modulation frequency of 0.2 GHz and chaos shifting key with a rate of 0.2 Gbit/s are numerically simulated, separately. The ratio of the signal to the absolute synchronous error and the time for achieving synchronous demodulation are analysed in detail. The results illustrate that the system has stronger privacy and good performances so that it can be applied in chaotic dual-directional high rate secure communications.[第一段]     

A novel hyperchaos evolved from three dimensional modified Lorenz chaotic system

This paper reports a new four-dimensional continuous autonomous hyperchaos generated from the Lorenz chaotic system by introducing a nonlinear state feedback controller. Some basic properties of the system are investigated by means of Lyapunov exponent spectrum and bifurcation diagrams. By numerical simulating, this paper verifies that the four-dimensional system can evolve into periodic, quasi-periodic, chaotic and hyperchaotic behaviours. And the new dynamical system is hyperchaotic in a large region. In comparison with other known hyperchaos, the two positive Lyapunov exponents of the new system are relatively more larger. Thus it has more complex degree.[第一段]     

Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincare surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy εc, for ε 〈 εc, the system is near-integrable, and as the decrease of ε the spectrum is gradually rendered regular and finally turns into a pure Coulomb field situation. On the contrary, if ε 〉 εc, with the increase of ε, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.     

All-optical chaotic MQW laser repeater for long-haul chaotic communications

We present an all-optical chaotic multi-quantum-well (MQW) laser repeater system to be used in long-haul chaotic communications. Chaotic synchronization is achieved among transmitter, repeater, and receiver. Chaotic repeater communications with a sinusoidal signal of 0.2-GHz modulation frequency and a digital signal of 0.4-Gb/s bit rate are numerically simulated, respectively. Calculation results illustrate that the signals are well decoded by the chaotic repeaters. Its bandwidth and the characteristics at much high bit rate are also analyzed. Simulation shows that the repeater can improve decoding quality, especially in higher bit rate chaotic communications.     

Anti-control of chaos in p--Ge photoconductor

We present a scheme for the anti-control of chaos in the p-Ge photoconductor system by using a chaotic laser to irradiate and disturb this system.The numerical simulations show that this scheme can be effectively used to control periodic states in this p-Ge system into chaotic states.Moreover,the different chaos states with different chaotic orbits can be obtained by appropriately adjusting the disturbance intensity and disturbance frequency,and by increasing this intensity or reducing this frequency,this p-Ge system gradually evolves to fully developed chaotic states.     

Time-Resolved Terahertz Spectroscopy with Free-Space Electro-Optic Sampling

We present a time-resolved ultrafast measurement in terahertz (THz) frequency region by means of the free-space electro-optic sampling. The fast delay scan technique is used to suppress the noise with low frequency and to improve the signal-to-noise ratio of the system. The transmission spectra of different materials are obtained.The optical properties of these materials in a THz region are shown. The broadening of spectrum and chirping phenomena are illustrated. We find that polystyrene is an excellent material for the THz application.     

Experimental Investigation of Chaos Synchronization in DFB Diode Lasers with Unsymmetrical Scheme

We experimentally generate high dimension chaotic waveforms with smooth spectrum using a distributed feedback （DFB） semiconductor laser with unidirectional fibre ring long-cavity feedback, and implement the stable chaos synchronization when the chaotic light is injected into a solitary DFB laser diode. The synchronization quality is investigated by time-domain and frequency-domain analysis separately, The frequency-domain analysis indicates that the synchronization has higher quality in the high frequency band. The influences of the injection strength and the frequency detuning on the synchronization are measured. Our experimental results show that the robust synchronization can be maintained with the optical frequency detuning from -11GHz to 40 GHz.     

Quantum coherence in A-three-level system driven by bichromatic coupling field

<正>We present a theoretical study of quantum coherent effects in a A-three-level system with a strong bichromatic coupling field and a weak probe field.When one component of the strong bichromatic coupling field is resonant with a corresponding transition and the other is detuning with an integer fraction of the Rabi frequency of the resonant field, the absorption spectrum exhibits a series of symmetrical doublets.While two frequencies of the strong bichromatic coupling field are symmetrically detuned from the transition,the position and the relative intensity of the absorption peak are both affected by the coupling field intensity and detuning.An explanation of the spectrum is given in term of the dressed-state formalism.     

The analysis of a novel 3-D autonomous system and circuit implementation

This Letter presents a new three-dimensional autonomous system with four quadratic terms. The system with five equilibrium points has complex chaotic dynamics behaviors. It can generate many different single chaotic attractors and double coexisting chaotic attractors over a large range of parameters. We observe that these chaotic attractors were rarely reported in previous work. The complex dynamical behaviors of the system are further investigated by means of phase portraits, Lyapunov exponents spectrum, Lyapunov dimension, dissipativeness of system, bifurcation diagram and Poincaré map. The physical circuit experimental results of the chaotic attractors show agreement with numerical simulations. More importantly, the analysis of frequency spectrum shows that the novel system has a broad frequency bandwidth, which is very desirable for engineering applications such as secure communications.     

一类多翼蝴蝶混沌吸引子及其电路实现

提出了一种构造多翼蝴蝶混沌吸引子的新方法,在Liu混沌系统的基础上,通过设计一种新的分段线性函数,构造了一个产生多翼蝴蝶混沌吸引子的混沌系统,对系统的平衡点、Lyapunov指数谱、分岔图、相图、频谱和Poincare截面进行了分析。最后,设计了相应的硬件电路,电路实验结果与数值仿真结果一致,验证了该方法的可行性和有效性。     

混沌信号在光纤传输过程中的非线性演化

对光纤混沌传输理论及混沌信号与光纤传输媒介相互作用的物理机制进行了理论研究. 通过耦合激光混沌系统和光纤传输信道，提出光纤混沌信号传输的非线性演化物理模型. 着重分析光纤自相位调制对激光混沌信号传输与演化的作用. 结果表明：自相位调制不影响混沌信号脉冲的形状，但能产生非线性相移使混沌信号频谱展宽；自相位调制不影响混沌信号脉冲的功率分布和场强分布，但能影响混沌信号脉冲的功率频谱分布，影响混沌信号光场以及慢变场的变化. 提出混沌信号在光纤传输中的非线性演化频率啁啾和形式，数值模拟了混沌信号在光纤传输过程中的相位、频谱、场以及场的慢变部分的相空间等演化形式和特点. 关键词： 混沌 光纤 传输 演化     

一个四翼混沌吸引子

在新的四维混沌系统中数值观察到四翼混沌吸引子，然而，通过进一步分析发现，该四翼吸引子并非真实的，实际上它是上、下两个共存的双翼混沌吸引子，他们各自有独立的混沌吸引域，由于其位置靠得太近和数值误差产生的一种假象.通过引入一个线性状态反馈控制项，系统的一些相似性被破坏，受控系统能产生穿越上下吸引域界限的对角双翼混沌吸引子，进一步，随着动力学模态的演化，上下混沌吸引子与对角混沌吸引子融合成一个真正的四翼混沌吸引子.最后，通过比较该四翼混沌吸引子的系统、Lorenz系统、Chua氏电路等混沌信号的频谱发现，四翼混沌吸引子的系统信号具有极宽的频谱带宽，该特性在通讯加密等工程应用中具有重要价值. 关键词： 四维混沌系统 双翼吸引子 四翼吸引子 频谱分析     

平坦宽带混沌激光的产生及同步

利用光纤环长外腔光反馈半导体激光器产生了频谱平坦的宽带混沌激光,其对应的激光频谱可有效地隐藏外腔的谐振频率,增加了系统的保密性.通过单向耦合方式,将产生的混沌激光注入到另一个参数相近的半导体激光器中,实现了平坦宽带混沌同步输出,两同步激光器输出的相关系数达到084.同时实验研究了注入强度和主从激光器的频率失谐对同步质量的影响,结果表明在强光注入锁定下,在很大频率失谐范围内均可实现同步,而且注入强度越大,主从激光器输出的相关系数越大,维持混沌同步所允许的频率失谐范围越大. 关键词： 混沌同步 单向光纤环 光反馈 半导体激光器     

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     

A new five-term simple chaotic attractor

A new chaotic attractor is presented with only five terms in three simple differential equations having fewer terms and simpler than those of existing seven-term or six-term chaotic attractors. Basic dynamical properties of the new attractor are demonstrated in terms of equilibria, Jacobian matrices, non-generalized Lorenz systems, Lyapunov exponents, a dissipative system, a chaotic waveform in time domain, a continuous frequency spectrum, Poincaré maps, bifurcations and forming mechanisms of its compound structures.     

Some comments on the Mindlin-Goodman method of solving vibrations problems with time dependent boundary conditions

Experimental evidence is presented for chaotic type non-periodic motions of a deterministic magnetoelastic oscillator. These motions are analogous to solutions in non-linear dynamic systems possessing what have been called “strange attractors”. In the experiments described below a ferromagnetic beam buckled between two magnets undergoes forced oscillations. Although the applied force is sinusoidal, nevertheless bounded, non-periodic, apparently chaotic motions result due to jumps between two or three stable equilibrium positions. A frequency analysis of the motion shows a broad spectrum of frequencies below the driving frequency. Also the distribution of zero crossing times shows a broad spectrum of times greater than the forcing period. The driving amplitude and frequency parameters required for these non-periodic motions are determined experimentally. A continuum model based on linear elastic and non-linear magnetic forces is developed and it is shown that this can be reduced to a single degree of freedom oscillator which exhibits chaotic solutions very similar to those observed experimentally. Thus, both experimental and theoretical evidence for the existence of a strange attractor in a deterministic dynamical system is presented.     

开关变换器离散子系统混沌点过程描述及EMI抑制

利用混杂系统理论将开关变换器描述为连续子系统和离散子系统的集合,由此根据混沌PWM规律,建立离散子系统的开关混沌点过程模型. 同时以常用的线性分段混沌映射实现混沌PWM控制,分析得出混沌PWM点过程的特征函数,概率密度函数,进一步得到混沌PWM和周期PWM的频谱特性. 论文的试验结果表明,输出电压稳定情况下混沌开关变换器,实现了谐波峰值的抑制,开关变换器EMI特性明显改善. 关键词： 混杂系统 开关变换器 混沌点过程 电磁干扰     

自调频混沌系统及其调频码耦合同步

提出了一个闭环自调频混沌系统, 对压控振荡器输出进行采样, 采样值经非线性变换后产生控制压控振荡器下一时刻频率的调频码. 利用一维分岔图、二维分岔图和Lyapunov指数等研究了该系统的动力学行为; 并利用峰值均值功率比、频谱以及输出信号的相关函数等分析了该系统的应用特性. 研究表明, 该系统有复杂的动力行为, 展现分岔、多稳态和混沌等现象, 产生的信号具有低峰值均值功率比和宽频带的特性. 同时还讨论了利用调频码实现系统同步的可能性, 证实了简单的控制器可以实现自调频系统的同步. 在电路实验中, 压控振荡器用数字频率合成技术实现, 实验结果与理论分析一致. 关键词： 混沌 多稳态 峰值均值功率比 同步