A non-autonomous chaotic system with no equilibrium

Recently, researchers showed that adding a stepwise control pulse to the Sprott C system (with two equilibrium points) can create a translational multi-butterfly attractor. In this research, a sinusoidal control pulse is added to a system with no equilibria. So, a non-autonomous chaotic system with no equilibria is designed and studied. The sinusoidal term causes an extension in the chaotic attractor. Dynamical behaviors of the proposed oscillator are studied. Bifurcation analysis by changing the frequency of the sinusoidal term shows its unbounded solution at some parameters. Also, bifurcation diagram of the oscillator by the force's strength is studied. Lyapunov exponents show that the oscillator has chaotic dynamics in the entire studied interval of force's strength. In addition, circuit implementation shows its feasibility.     

A novel memristive chaotic system without any equilibrium point

Various chaotic systems have been studied recently. They can show many different dynamics and features. A memristive 4D chaotic oscillator with no equilibria, multistability, and hidden attractor is presented in this paper. Chaotic attractor of the proposed oscillator is discussed, and its dynamical behaviors are investigated. The oscillator does not have any equilibrium. In addition, the phenomena of multistability is studied in this system. It shows chaotic dynamics and periodic windows, verified by Lyapunov exponents’ diagram. Image encryption is studied as an engineering application of the system. The proposed system has a proper performance in encryption. Finally, this memristive chaotic system is realized using FPGA.     

Simple RC chaotic oscillator

An RC oscillator exhibiting chaotic behaviour is described. It contains two opamps, a Wien bridge and a diode used as a nonlinear device. The typical waveforms, the phase portraits, the power spectra and the correlation dimension of the attractor are presented to illustrate the chaotic oscillations     

Simple 4D chaotic oscillator

An extremely simple 4D chaotic oscillator is presented. It contains a single op amp, two LC circuits and a diode used as a nonlinear device. The chaotic oscillations have been characterised using the correlation dimension of the strange attractor, the Lyapunov exponents and the Lyapunov dimension. The dimensions are found to be >3     

三维多涡卷Colpitts混沌系统及其数字硬件实现

基于混沌吸引子形成的机理,利用单位锯齿波函数改造混沌Coipitts振荡器模型,提出了一个新三维多涡卷混沌系统,生成了(2K+1)涡卷混沌吸引子.单位锯齿波函数的引入,增加了系统的指数2平衡点,从而形成多涡卷吸引子.采用常规的动力学分析方法,研究了该多涡卷混沌系统的动力学特性,研究结果表明所提出的系统的Hopf分岔点仅...     

Test of the deterministic conjecture for the instantaneous time phase fluctuations of an oscillator

The fluctuations observed by recording the picosecond pulses of a mode-locked laser with a synchroscan streak camera are due to the laser jitter and to the variations of the zero crossing of the synchronization. By means of a simple model, it is shown that the dispersions measured when the synchronization is generated from the mode-locker oscillator reflect the instantaneous time phase fluctuations of this oscillator. From the study of the experimental recordings with methods of time series analysis it results that the phase noise of the electronic oscillator is consistent with an underlying low-dimensional strange attractor.     

Chaos generator via Wien-bridge oscillator

A new chaos generator obtained by designing a controller for the celebrated Wien-bridge oscillator is presented. The chaotic attractor exhibited in this generator is globally attractive and stable in the Liapunov sense and is more practical for engineering problems     

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     

一种强噪声背景下微弱信号检测方法研究

针对常规单混沌振子微弱信号检测方法存在检测过程不稳定的现象,将混沌吸引子与双振子差分检测技术相结合,提出一种通过调整系统稳定混沌态来检测微弱信号的改进方法,同时利用双差分振子来判别系统混沌态向周期状态转变的临界值。通过仿真分析,该方法可有效防止误判且实时性较好,有利于在强噪声背景下的微弱信号检测,为工程实际应用提供了一种可借鉴的方法。     

FPGA implementation of a chaotic oscillator with odd/even symmetry and its application

We propose a mathematical system capable of exhibiting chaos with a chaotic attractor which is odd symmetrical in the x − y phase plane but even symmetrical in the x − z and y − z phase planes respectively. A hardware implementation of the system is done on a digital FPGA platform for verification. The system is also attractive in the sense that (i) its dynamics are single-parameter controlled and (ii) it inherently generates two chaotic clock signals. As an application, an FPGA design methodology using this oscillator for speech encryption is demonstrated. The security of the proposed encryption scheme is evaluated and results confirm its robustness. Due to the efficient hardware resource utilization, the encrypted system delivers a throughput of 1.3Gbit/sec using a Xilinx Kintex 7.     

On the generation of CCII and ICCII oscillators from three Op Amps oscillator

A new quadrature oscillator using two current conveyors (CCII) and two inverting current conveyors (ICCII) is generated from a three Op Amp two integrator loop oscillator. The proposed oscillator is generalized and it is found that it is a member of a family of 64 oscillator circuits using combination of CCII and ICCII. Four of the reported oscillators are floating. The three Op Amps oscillator is also found to be the reference oscillator circuit in the generation of two basic CCII two integrator loop grounded passive element oscillators. The nodal admittance matrix (NAM) expansion is used to show the basic steps in the generation of the two alternatives CCII grounded passive element oscillators. Each of the two CCII oscillators is a member of a family of sixteen oscillator circuits using combination of CCII and ICCII. Two of the reported oscillators are floating and their adjoint oscillator circuits are not floating. Simulation results are included.     

吸引子分析与核爆地震模式识别

本文利用从时域地震信号中提取的各种特征值来构造相空间,对四组样本进行的结果发现,在该相窨中两个“吸引子”;地下核爆炸吸引子和天然在震吸引子,求得吸引子的关联维数均为分数维,且小于相空间的维数,当相空间的维数从低到高增加时,吸引子维数明显出现饱和值;不同吸引子的分维数不同,本文还提出了“吸引中心”的概念,并就吸引子、吸引子数、吸引中心和吸引域等在核爆地震模式识别中的应用问题进行了探讨。     

硅振荡器的抗高过载实验设计与分析

硅振荡器是一种在高过载条件下有可能代替石英晶体振荡器为应用系统提供稳定时钟的振荡器。对硅振荡器开展高过载实验研究,具有重要的应用价值。论文以LTC6909I型硅振荡器为实验对象,对高过载环境下可能产生的频率漂移及是否损坏这两个主要方面进行了实验研究。实验证明了硅振荡器能经受高过载环境的考验,可以代替石英晶体振荡器为应用系统提供稳定时钟。     

Intensity noise in ASK coherent lightwave receivers

The effect of local oscillator intensity noise on the performance of two and three-branch ASK homodyne receivers and single-branch ASK heterodyne receivers is investigated and an optimum local oscillator power is found. At optimum local oscillator power, both the three-branch and heterodyne receivers are found to have a somewhat better sensitivity than the two-branch receiver. If the local oscillator power is high than the optimum value, the three-branch receiver is significantly less sensitive to intensity noise than the other two receivers     

Current conveyor-based voltage-mode two-phase and four-phase quadrature oscillators

A voltage mode two-phase quadrature oscillator using plus-type second generation current conveyors [CCIIs(+)] is realized by using a simple technique. The basic building block for this technique is a voltage mode non-inverting band-pass filter. The two-phase quadrature oscillator is then transformed into a four-phase quadrature oscillator by replacing the two CCIIs(+) by two dual output, current conveyors [DO-CCIIs]. The proposed circuits enjoy attractive features such as use of grounded passive components, independent frequency control, outputs of almost equal magnitude and low sensitivity figures. Both the oscillator circuits are designed and verified using PSPICE simulation.     

Dynamical diseases of brain systems: different routes to epileptic seizures

In this overview, we consider epilepsies as dynamical diseases of brain systems since they are manifestations of the property of neuronal networks to display multistable dynamics. To illustrate this concept we may assume that at least two states of the epileptic brain are possible: the interictal state characterized by a normal, apparently random, steady-state electroencephalography (EEG) ongoing activity, and the ictal state, that is characterized by paroxysmal occurrence of synchronous oscillations and is generally called, in neurology, a seizure. The transition between these two states can either occur: 1) as a continuous sequence of phases, like in some cases of mesial temporal lobe epilepsy (MTLE); or 2) as a sudden leap, like in most cases of absence seizures. In the mathematical terminology of nonlinear systems, we can say that in the first case the system's attractor gradually deforms from an interictal to an ictal attractor. The causes for such a deformation can be either endogenous or external. In this type of ictal transition, the seizure possibly may be anticipated in its early, preclinical phases. In the second case, where a sharp critical transition takes place, we can assume that the system has at least two simultaneous interictal and ictal attractors all the time. To which attractor the trajectories converge, depends on the initial conditions and the system's parameters. An essential question in this scenario is how the transition between the normal ongoing and the seizure activity takes place. Such a transition can occur either due to the influence of external or endogenous factors or due to a random perturbation and, thus, it will be unpredictable. These dynamical changes may not be detectable from the analysis of the ongoing EEG, but they may be observable only by measuring the system's response to externally administered stimuli. In the special cases of reflex epilepsy, the leap between the normal ongoing attractor and the ictal attractor is caused by a well-defined external perturbation. Examples from these different scenarios are presented and discussed.     

Practical Design and Evaluation of Fractional-Order Oscillator Using Differential Voltage Current Conveyors

This paper deals with the design, analysis, computer simulation, and experimental measurement of fractional-order sinusoidal oscillator with two current conveyors, two resistors, and two fractional immittance elements. The used conveyor is based on the bulk-driven quasi-floating-gate technique in order to offer high threshold-to-supply voltage ratio and maximum input-to-supply voltage ratio. The supply voltage of the oscillator is 1 V, and the power consumption is \(74\,\upmu \hbox {W}\), and hence the proposed oscillator can be suitable for biomedical, portable, battery-powered, and other applications where the low-power consumption is critical. A number of equations along with graphs describing the theoretical properties of the oscillator are presented. The unique features of fractional-order oscillator are highlighted considering practical utilization, element computation, tuning, phase shift of output signals, sensitivities, etc. The simulations performed in the Cadence environment and the measurements of a real chip confirm the attractive features of the proposed oscillator.     

Concurrent Dual-Frequency Oscillators and Phase-Locked Loops

A dual-frequency oscillator employing a fourth-order tank is shown to have the ability to generate simultaneous oscillations at two frequencies. A nonlinear analysis to determine the steady-state and transient behavior of this oscillator is presented. Further, the phase-noise expression for the dual-frequency oscillator is derived and compared with that of a single-frequency oscillator. A dual-loop phase-locked loop (PLL) is designed to lock the frequencies of the dual-frequency oscillator to two external references independently. A prototype of a dual-frequency voltage-controlled oscillator (VCO) along with the dual-loop PLL is implemented in a BiCMOS SiGe technology. The dual-frequency VCO oscillates simultaneously at 2.33 and 4.98 GHz with 12.5% and 10.3% tuning ranges, respectively. The PLL has locking ranges of 4.2% and 3.6% for 2.33 and 4.98 GHz, respectively. Potential applications of concurrent multifrequency oscillators in multifunctional communication systems and multiband beam forming are discussed.      

On the use of a digital computer as a two-phase variable-amplitudevariable-frequency oscillator

A feasibility study on the use of a digital computer as a variable-amplitude variable-frequency oscillator which generates two-phase sinusoidal excitation control signals for a dual-excited synchronous generator is described. The oscillator uses two input signals. One input signal is used to control the frequency of the oscillator outputs, and the other is used to control their amplitudes. By a single variable, the software can be configured to vary the oscillator frequency range and to greatly reduce (almost eliminate) the harmonic distortion of the output signals. The harmonic distortion is constant and independent of the output frequency for each possible oscillator frequency range. The software-based oscillator design is flexible and can be used to generate different types of multiphase signal waveforms     

On the realization of circuit-independent nonautonomous pulse-excited chaotic oscillator circuits

The aim of this paper is to present a simple circuit design method for realizing a nonautonomous chaotic oscillator given a second-order sinusoidal oscillator with two capacitors. The proposed method relies on applying a periodic pulse train, as an exciting source, and the addition of a signum-type nonlinear transconductor to the given sinusoidal oscillator. Experimental results of designed circuits are shown.