分数阶Lorenz系统的分析及电路实现

频域传递函数近似方法不仅是常用的 分数阶混沌系统相轨迹的数值分析方法之一, 而且也是设计分数阶混沌系统电路的主要方法. 应用该方法首先研究了分数阶Lorenz系统的混沌特性, 通过对Lyapunov指数图、分岔图和数值仿真分析, 发现了其较为丰富的动态特性, 即当分数阶次从0.7到0.9以步长0.1变化时, 该分数阶Lorenz系统既存在混沌特性, 又存在周期特性, 从数值分析上说明了在更低维的Lorenz系统中存在着混沌现象. 然后又基于该方法和整数阶混沌电路的设计方法, 设计了一个模拟电路实现了该分数阶Lorenz系统, 电路中的电阻和电容等数值是由系统参数和频域传递函数近似确定的. 通过示波器观测到了该分数阶Lorenz系统的混沌吸引子和周期吸引子的相轨迹图, 这些电路实验结果与数值仿真分析是一致的, 进一步从物理实现上说明了其混沌特性. 关键词： 分数阶系统 Lorenz系统 分岔分析 电路实现     

单参数Lorenz混沌系统的电路设计与实现

为了研究混沌系统的性质及其应用,采用分立元件设计并实现了单参数Lorenz混沌系统,系统参数与电路元件参数一一对应.通过调节电路中的可变电阻,观察到了该单参数系统的极限环、叉式分岔、倍周期分岔和混沌等动力学现象,以及该系统由倍周期分岔进入混沌的过程.研究了分数阶单参数Lorenz系统存在混沌的必要条件,找出了分数阶单参数Lorenz系统出现混沌的最低阶数以及最低阶数随系统参数变化的一般规律.电路仿真与电路实现研究表明,单参数Lorenz系统具有物理可实现性、丰富的动力学特性以及理论分析与实验结果的一致性.     

Circuit implementation and multiform intermittency in ahyper-chaotic model extended from Lorenz system

<正>This paper presents a non-autonomous hyper-chaotic system,which is formed by adding a periodic driving signal to a four-dimensional chaotic model extended from the Lorenz system.The resulting non-autonomous hyper-chaotic system can display any dynamic behaviour among the periodic orbits,intermittency,chaos and hyper-chaos by controlling the frequency of the periodic signal.The phenomenon has been well demonstrated by numerical simulations,bifurcation analysis and electronic circuit realization.Moreover,the system is concrete evidence for the presence of Pomeau-Manneville Type-Ⅰintermittency and crisis-induced intermittency.The emergence of a different type of intermittency is similarly subjected to the frequency of periodic forcing.By statistical analysis,power scaling laws consisting in different intermittency are obtained for the lifetime in the laminar state between burst states.     

Characteristics of dual element ultrasonic transducers in the long pulse radiation mode

The frequency and transfer characteristics of dual element ultrasonic transducers are theoretically and experimentally investigated in the long pulse radiation mode for the case where one of the piezoelectric elements is connected to a control circuit in the form of an inductance coil or a resistor. For the controlled damper and controlled layer cases, the characteristic features of radiation as functions of the control circuit parameters are determined, as well as the conditions for an increase in ultrasonic wave radiation power. With certain conditions being satisfied, we demonstrate the possibility of amplitude modulation of the emitted ultrasonic wave by periodic switching of control circuit elements.     

Determination of the equivalent circuit of gunn-elements for X-band oscillator applications

The main purpose of this paper is to develope a procedure for the computer-aided determination of the equivalent circuit of Gunn-elements. In order to determine the equivalent circuit, the Gunne-element is first measured in a test oscillator. Varying the elements of the circuit the calculated frequency and power distribution is adjusted to the measured one by means of an iterative method. The equivalent circuit of Gunn-elements obtained in this way is used for the dimensioning of Gunn-element-oscillators in the X-band in finline technique.     

Fuzzy modeling and synchronization of different memristor-based chaotic circuits

This Letter is concerned with the problem of fuzzy modeling and synchronization of memristor-based Lorenz circuits with memristor-based Chua?s circuits. In this Letter, a memristor-based Lorenz circuit is set up, and illustrated by phase portraits and Lyapunov exponents. Furthermore, a new fuzzy model of memristor-based Lorenz circuit is presented to simulate and synchronize with the memristor-based Chua?s circuit. Through this new fuzzy model, two main advantages can be obtained as: (1) only two linear subsystems are needed; (2) fuzzy synchronization of these two different chaotic circuits with different numbers of nonlinear terms can be achieved with only two sets of gain K. Finally, numerical simulations are used to illustrate the effectiveness of these obtained results.     

Chaos in fractional-order generalized Lorenz system and its synchronization circuit simulation

The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.     

一个新四维非自治超混沌系统的分析与电路实现

在以Lorenz系统为基础的一个新超混沌系统上,加入一个驱动信号,组成了一个四维非自治超混沌系统.该系统基本动力学特性的变化,主要是通过控制外界输入信号的频率实现的.在不同的频率参数下,该系统体现出了周期轨、二维环面、混沌以及超混沌不同的动力学特性,其中周期轨特性较为显著.这个现象在数值仿真以及分形分析上得到了很好地验证.最后设计一个模拟电路,通过实验结果进一步验证了与数值仿真的一致性.     

一个超混沌Lorenz吸引子及其电路实现

通过在三阶Lorenz系统中引入一个外加的状态变量构造了一个新的超混沌系统.对系统的一些基本特性，如耗散性、平衡点、稳定性、Hopf分叉进行了详细分析，且观察到了从周期到混沌、超混沌的演化.系统超混沌的存在性通过Lyapunov指数谱得到了验证.还设计了一个模拟电子电路，从电路实验中观察到了各种超混沌吸引子. 关键词： Lorenz系统 超混沌吸引子 电路实现     

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     

Open-loop frequency response for a chaotic masking system

In this paper, a new numerical simulation approach is proposed for the study of open-loop frequency response of a chaotic masking system. Using Chua's circuit and the Lorenz system as illustrative examples, we have shown that one can employ chaos synchronization to separate the feedback network from a chaotic masking system, and then use numerical simulation to obtain the open-loop synchronization response, the phase response, and the amplitude response of a chaotic masking system. Based on the analysis of the frequency response, we have also proved that changing the amplitude of the exciting (input) signal within normal working domain does not influence the frequency response of the chaotic masking system. The new numerical simulation method developed in this paper can be extended to consider the open-loop frequency response of other systems described by differential or difference equations.     

频率自动跟踪超声波电源设计

针对超声波电源工作时负载状态改变,换能系统产生谐振漂移的问题,提出了一种基于STM32的频率自动跟踪超声波电源的设计。电源逆变电路采用带辅助网络的全桥结构,阻抗匹配电路选择了一种改进型的T型匹配网络,应用PWM移相调功技术控制电源的输出功率,通过数字鉴相技术得到电压电流的相位差作为电路谐振状态的反馈信号,结合STM32主控制器进行PI控制,调节PWM波的输出频率使电路始终工作于谐振状态,实现了谐振频率的自动跟踪。最后基于该设计方案,实际制作了一款应用于超声波清洗仪的电源,并通过实验验证了该电源具有输出功率稳定,负载适应性强,输出频率自动跟踪等特点。     

一类自治混沌系统的动力学分析与电路实现

分析讨论一类新的三维二次自治混沌系统.通过理论分析、数值仿真,计算系统的Lyapunov指数谱和Lyapunov维数,以及系统的分岔图等,对系统的基本动力学特性进行分析.设计实现该系统的混沌电路,建立系统参数和电路参数的对应关系,运用Pspice软件对电路进行仿真实验,证实分析的正确性.所讨论的系统不同于Lorenz系统、Rössler系统、Chen系统和Lü系统等,且电路实现很简单实用.     

SYSTEMATICS OF THE PERIODIC WINDOWS IN THE LORENZ MODEL AND ITS RELATION WITH THE ANTISYMMETRIC CUBIC MAP

The Lorenz model and the antisymmetric cubic map enjoy the same discrete symmetry. A careful study of a one-dimensional bifurcation diagram ob- tained numerically from the Lorenz model reveals that the systerriatics of periodic windows is closely related to that of the cubic map. In addition, we determined the drift of the fundamental frequency and thus proposed a nomenclature for the periodic windows by associating an absolute period to each window, which in turn agrees with the corresponding word made of three letters for most of the observed periods.     

Investigation of magnetoimpedance effect on electrodeposited NiFe/Cu wire using inductance spectroscopy

In this report, inductance spectroscopy (IS) has been used as a tool to investigate the thickness dependence of magnetoimpedance (MI) on electrodeposited NiFe thin films. An MI value as high as 140% has been observed under an applied magnetic field of 76 Oe at 300 kHz frequency for a film thickness of 6.8 μm. This result is in sharp contrast to earlier reports in literature showing monotonous increase in MI as a function of thickness. Maximum of MI was found at an optimum film thickness whose position varies with frequency. These reports exhibiting strong frequency dependence of MI prompted us to investigate the underlying physics using IS. The origin of MI lies in the combined effect of domain wall motion and spin rotation, which contributes to permeability. A parallel inductance and resistance (LR) circuit in series with series LR circuit model has been proposed as an equivalent electrical model to describe the property of these coated wires. The circuit elements have been linked with the phenomenon of domain wall motion and spin rotation. The experimental results obtained appear to be consistent with the proposed equivalent circuit model.     

一种小型铷原子频标功率稳幅电路

传统的铷原子频标（RAFS）射频电路所采用的饱和输出的方式虽然能稳定射频信号幅度,但是无法稳定射频信号波形,导致微波功率稳定性不够理想．本文介绍了一种铷原子频标微波功率稳幅电路方案,该方案以阶跃恢复二极管（SRD）的偏置电压为参考,通过控制可变增益放大器（VGA）的增益实现自动增益控制（AGC）．该方案在控制射频信号幅度的同时亦控制其波形．结果表明该方案能有效改善铷原子频标的微波信号功率的稳定性．     

Circuit bounds on stochastic transport in the Lorenz equations

In turbulent Rayleigh–Bénard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by the Rayleigh number. In experiments, one measures the Nusselt number for a given Rayleigh number, and the question of how close that value is to the maximal transport is a key prediction of variational fluid mechanics in the form of an upper bound. The Lorenz equations have traditionally been studied as a simplified model of turbulent Rayleigh–Bénard convection, and hence it is natural to investigate their upper bounds, which has previously been done numerically and analytically, but they are not as easily accessible in an experimental context. Here we describe a specially built circuit that is the experimental analogue of the Lorenz equations and compare its output to the recently determined upper bounds of the stochastic Lorenz equations [1]. The circuit is substantially more efficient than computational solutions, and hence we can more easily examine the system. Because of offsets that appear naturally in the circuit, we are motivated to study unique bifurcation phenomena that arise as a result. Namely, for a given Rayleigh number, we find a reentrant behavior of the transport on noise amplitude and this varies with Rayleigh number passing from the homoclinic to the Hopf bifurcation.     

超微粒金刚石砂轮电解修整电源的研制

在轨迹成型法加工光学零件技术中 ,为了实现超精密磨削 ,采用了在线电解修整砂轮技术。为此研制了高频脉冲电源 ,研制的高频脉冲电源用于电解修整金属结合剂金刚石砂轮。高频电源由主电路、接口电路和控制电路组成。主电路是提供工作电流的通路 ,控制电路采用了单片机控制技术 ,接口电路实现A/D转换及驱动电压放大级。经调试电源电压在 0～ 90V ,脉冲频率在 4～ 5 0 0Hz范围内可调 ,平均电流可达 15A。该电源的技术指标 ,均达到设计要求。     

Sequences of gluing bifurcations in an analog electronic circuit

We report on the experimental investigation of gluing bifurcations in the analog electronic circuit which models a dynamical system of the third order: Lorenz equations with an additional quadratic nonlinearity. Variation of one of the resistances in the circuit changes the coefficient at this nonlinearity and replaces the Lorenz route to chaos by a different scenario which leads, through the sequence of homoclinic bifurcations, from periodic oscillations of the voltage to the irregular ones. Every single bifurcation “glues” in the phase space two stable periodic orbits and creates a new one, with the doubled length: a sequence of such bifurcations results in the birth of the chaotic attractor.     

一类耦合非线性振子同步混沌Hopf分岔及其电路仿真

对于一类同时存在扩散耦合和梯度耦合的非线性振子系统, 通过空间傅里叶变换，得到具有不同波矢的各运动模式的相互独立的运动方程. 计算各横截模的Lyapunov指数, 可在耦合参数平面上确定同步混沌的稳定区域. 在稳定区域边界, 一对共轭横截模式失稳，导致同步混沌的Hopf分岔. 对耦合Lorenz振子系统进行了数值模拟，并设计了耦合Lorenz振子系统的电路, 进行耦合振子系统同步混沌Hopf分岔的电路仿真实验. 计算和仿真的结果表明，Hopf分岔的特征频率等于失稳横截模式的振荡频率. 关键词： 耦合非线性振子 同步混沌 横截模式 电路仿真