Synchronization and chaos in coupled memristor-based FitzHugh-Nagumo circuits with memristor synapse

The memristor has drawn a significant interest in the fields of neuromorphic circuits because the nanoscale memristor is a strong candidate to become the critical element of novel ultra-high density low-power non-volatile memories. In the present paper, we focus on networks of FitzHugh-Nagumo neuron circuits employing memristor. First, we build the memristor-based circuit of FitzHugh-Nagumo model. The details of the chaotic phenomena of the memristor-based FitzHugh-Nagumo circuit under external stimuli have been found with use of computer simulations, i.e., we have numerically calculated waveform diagrams, phase portraits, Lyapunov exponents and bifurcation diagram. And we also confirm these results of theoretical analyses and numerical calculations by circuit simulation experiments of the actual analog circuit realization using Multisim modeling. Then the synchronization of coupled memristor-based chaotic neurons with memristor synapse is discussed, and synchronization mechanism is also found. Finally, we have also derived the sufficient conditions of chaotic synchronization in unidirectional coupled neuron circuits and bidirectional coupled neuron circuits respectively, which are that the parameter of memristor synapse must meet certain conditions. These results of theoretical analyses have been confirmed by numerical simulation.     

基于滤波器和忆阻二极管桥的振荡器实验方案与验证

非线性普遍存在于实际电路中。本文基于Sallen-Key滤波器和忆阻二极管桥设计了一类忆阻振荡器电路。并以一个忆阻振荡器为例，制定了实验方案，完成了实验验证。结果表明，通过改变电路元件参数值，可观测到周期极限环、准周期振荡以及混沌振荡等非线性现象。该电路结构简单，调试方便，现象丰富。该实验方案可作为本科课程设计的重要研究性内容，加深学生对电路中非线性现象的理解。     

Hyperchaotic spiking oscillators with periodic pulse-train input

This paper studies simple spiking oscillators with periodic pulse-train input. The circuits are piecewise linear and a normal form circuit equation is derived in order to extract essential parameters. The return map and its Jacobian matrix can be described precisely. If the input is not present, the circuits can exhibit hyperchaotic and periodic attractors. As the input is applied, the attractors can be changed into various periodic, chaotic and hyperchaotic attractors. The phenomena are characterized by Lyapunov exponents of the return map. Typical phenomena can be confirmed experimentally. These results provide basic information for analysis of bifurcation phenomena and application to pulse-coupled networks.     

Sights and sounds of chaos [autonomous and nonautonomous circuits]

The concept of chaos is introduced using actual circuit experiments. Several well-known chaotic circuits are used as vehicles to demonstrate the many phenomena associated with chaos. They are divided into two classes, autonomous and nonautonomous. For the simplest autonomous circuits the authors examine strange attractors, the Lorenz circuit, Lyapunov exponents, and fractals. For the simplest nonautonomous circuits they consider period-doubling, the two-dimensional Poincare cross section, the Devil's staircase, and phase-locked loops     

Les phénomènes chaotiques non linéaires? ćest très simple… au début

Chaos is observed in digital or analog non linear circuits of common use. Analyzing such circuits seems at first very easy but as soon as theoretical and experimental studies need more accurate calculation and more precise measurements, difficulties become rapidly untractable. Classical methods, like piecewise non linear analysis allow comprehensive calculation of the response of a non linear analog circuit. Two state variables lead to results of little complexity, however introducing a third variable staggers the difficulties in such a way that chaos may appear. Examples given in this paper introduce chaotic phenomena which at first appear very elementary. They shall illustrate lectures introducing the difficulties of non linear circuit analysis given to student engineery.     

Integrated Circuits of Map Chaos Generators

A chaotic noise is one of the most important implements for information processing such as neural networks. It has been suggested that chaotic neural networks have high performance ability for information processing. In this paper, we report two designs of a compact chaotic noise generator for large integration circuits using CMOS technology. The chaotic noise is generated using map chaos. We design both of the logistic map type and the tent map type circuits. These chaotic noise generators are compact as compared with the other circuits. The results show that the successful chaotic operations of the circuits because of the positive Lyapunov number. We calculate the Lyapunov exponents to certify the results of the chaotic operations. However, it is hard to estimate its accurate number for noisy data using the conventional method. And hence, we propose the modified calculation of the Lyapunov exponent for noisy data. These two circuits are expected to be utilized for various applications.     

Stabilizing unstable equilibria of chaotic systems from a State observer approach

In this paper, a simple control method is proposed for stabilizing unstable equilibria of two typical classes of chaotic systems. For piecewise-linear chaotic systems, such as Chua's circuit, the control parameters can be selected via the pole placement technique from the linear control theory. For general nonlinear chaotic systems with continuously differentiable nonlinearities, particularly polynomial chaotic systems such as the Ro/spl uml/ssler system, Lorenz system, Chen's system, and the modified Chua's circuit with cubic nonlinearity, the control parameters can be chosen according to the pole placement technique and some additional theories of nonlinear ordinary differential equations. The criteria for the design of the control parameters are also investigated. This method is demonstrated to be highly robust against system parametric variations. To verify the effectiveness of the method, it is applied to both the original and the modified chaotic Chua's circuits, where satisfactory control performance is observed in simulations.     

二维混沌信号产生器的设计

混沌电路设计是混沌通信和混沌加密等应用的先决条件,因此混沌电路的理论研究和设计具有十分重要的意义.本文提出混沌电路的一种新的设计方法,可以在二维空间中简单灵活的设计构造出一类混沌系统.该方法的最大优点是:采用模块化设计思路,混沌吸引子的形状可以根据实际需要来设计,易于电路和集成电路实现.     

锁相鉴频器混沌现象的研究

该文研究无线电技术与现代通信领域广泛使用的锁相鉴频器中的混沌现象,利用Melnikov方法,证明了当输入信号参数、系统参数满足一定条件时,锁相鉴频器有混沌信号输出。通过电路实验,从频谱分析仪上观察到电路出现混沌时,压控振荡器输出端的连续频谱,进一步证实了锁相鉴频器电路中存在混沌现象。实验结果与理论分析相吻合,文中的结论对实际设计和应用锁相鉴频器,具有重要的指导意义。     

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.     

Keeping chaos at bay

The use of electronic circuits in studying chaotic dynamics and control are reviewed. Since all chaotic systems have several properties in common, simple circuits are analogous to much more complicated ones, such as lasers. Consequently, the methods developed to control chaos in electronic circuits are applicable to many diverse physical systems. The controlling device itself is a high-speed analog circuit. In applying perturbations, no calculations are made; instead, trial-and-error adjustments are used to locate the desired behavior. The initial observations of chaos in electronics, the development of the Ott-Grebogi-Yorke method for calculating the perturbations needed to stabilize a periodic orbit in a chaotic system and the occasional proportional feedback method, and their applications are discussed     

光纤激光器的混沌现象分析

利用混沌理论对光纤激光器的稳定性进行了分析 ,由此得到了避免出现混沌现象的条件 ,为提高光纤激光器的稳定性提供了理论指导。在实验中观察到阵发混沌现象的发生 ,并用理论分析得出的结论对光纤激光器进行调整 ,最终避免了混沌现象的发生。     

Electronic simulation and microcontroller real implementation of an autonomous chaotic and hyperchaotic system made of a Colpitts-Josephson junction like circuit

Most of the simple Josephson junction (JJ) based circuits with chaotic behavior found in the literature are nonautonomous. Hyperchaotic JJ-based circuits are often either driven by an external force or result from coupling chaotic circuits. An autonomous simple circuit based on Josephson junction active element (JJ), with exactly three physical energy storage tanks, is proposed and analyzed in this paper. This Colpitts-like CLC circuit, though operating at low frequencies, can generate hyperchaotic signals when its nonlinear element is a resistive–capacitive–inductance shunted junction (LRCLSJ) model. Two equilibrium points are found, and their stability analysis is investigated. The proposed circuit displays Hopf bifurcation, periodic oscillations, chaotic and hyperchaotic attractors. The electronic implementation of the proposed circuit using OrCAD-PSpice software is presented to confront the numerical simulations results. A good qualitative agreement is revealed by comparing the analog and numerical simulations results. At last, the microcontroller real implementation is presented using Arduino UNO board. The results obtained are in good agreement with the numerical simulation results.

     

激光二极管泵浦的Nd~（3＋）：YVO_4内脏倍频激光器的稳态、反相态及混沌态输出研究

报道了激光二极管泵浦、内腔倍频、各向异性晶体Ｎｄ３＋：ＹＶＯ４激光器的输出特性．包括稳态、反相态以及混沌态研究结果，并根据理论模型对这些运转状态进行数值分析，理论计算与实验结果十分吻合。     

单环掺铒光纤激光器光延迟反馈的混沌控制

为了找到更加简单稳定激光系统的混沌化方法,采用光延迟反馈方法对单环掺铒光纤激光器特性进行了数值仿真,得到了各种周期现象而且产生了混沌现象。结果表明,利用单模单环掺铒光纤激光器,在附加光延迟反馈环路的方法下可以实现混沌控制。这一结果对应用于保密通信的混沌化简化具有重要意义。     

A New Approach to Analysis and Design of Chaos-Based Random Number Generators Using Algorithmic Converter

This paper presents a new approach to analysis and design of ADC-based random number generators. To this end, different full-bit and half-bit redundant stages of algorithmic converter are used to design chaotic maps. It is shown that, in the redundant and nonredundant structures, output probability density function of the converter stages and their related chaotic functions always converge to uniformity. It is demonstrated that residues become independent and uniformly distributed. This fact leads to the randomness and uniformity of distribution of the random number generator output bits. Moreover, it is shown that some common chaotic maps that are employed in chaotic random number generators can be implemented using nonredundant and half-bit redundant stages of algorithmic converter. In this way, the capability of ADC-based generators in designing chaotic maps and producing random number sequences is illustrated. The validity of the proposed chaos-based random number generator is confirmed using NIST statistical tests even in the presence of nonidealities in algorithmic converter. Since the ADCs are mixed-signal integrated circuits and can be used in high-speed applications, the ADC-based random number generator has high throughput and is easily embeddable in all analog and digital circuits.     

微波Colpitts混沌电路实验研究

本文首先介绍了Colpitts电路的数学模型，给出了基于预设定频谱分布的Colpitts混沌电路中主要电路参数的设计方法；然后对工作在微波频段的Colpitts混沌电路进行了实验研究，验证了给出的电路参数设计方案；最后对实验过程中的电路调试方法，电路频谱宽度的瓶颈问题，电路功耗问题以及进一步的工作进行了讨论。     

Emergent spiking in non-ideal memristor networks

Memristors have uses as artificial synapses and perform well in this role in simulations with artificial spiking neurons. Our experiments show that memristor networks natively spike and can exhibit emergent oscillations and bursting spikes. Networks of near-ideal memristors exhibit behaviour similar to a single memristor and combine in circuits like resistors do. Spiking is more likely when filamentary memristors are used or the circuits have a higher degree of compositional complexity (i.e. a larger number of anti-series or anti-parallel interactions). 3-memristor circuits with the same memristor polarity (low compositional complexity) are stabilised and do not show spiking behaviour. 3-memristor circuits with anti-series and/or anti-parallel compositions show richer and more complex dynamics than 2-memristor spiking circuits. We show that the complexity of these dynamics can be quantified by calculating (using partial auto-correlation functions) the minimum order auto-regression function that could fit it. We propose that these oscillations and spikes may have similar phenomena to brainwaves and neural spike trains and suggest that these behaviours can be used to perform neuromorphic computation.     

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.     

一种单输入控制器下的忆阻混沌同步电路设计与实现

该文提出一种在单输入控制器下基于忆阻器的混沌同步模拟电路设计及其实现方法,并将它应用于基于忆阻混沌同步的保密通信.首先,基于混沌同步理论,构建了混沌同步系统及保密通信模型,并设计实现了一种4阶压控忆阻混沌电路和混沌加密解密电路.其次,将所设计的忆阻混沌电路作为混沌驱动和响应电路,根据它们的误差系统设计了一种单输入混沌同...