A novel current-controlled memristor-based chaotic circuit

In this paper, a novel third-order autonomous memristor-based chaotic circuit is proposed. The circuit has simple topology and contains only four elements including one linear negative impedance converter-based resistor, one linear capacitor, one linear inductor, and one nonlinear current-controlled memristor. Firstly, the voltage-current characteristic analysis of the memristor emulator for different driving amplitudes and frequencies are presented. With dimensionless system, the symmetry, equilibrium point and its stability are analysed. It is shown that the system has two unstable saddle-foci and one unstable saddle. A set of typical parameters are chosen for the generation of chaotic attractor. Differing from the common period-doubling bifurcation route in smooth dynamical systems, this memristive system shows abrupt transition from the coexisting period-1 limit cycles to robust chaos when varying system parameters. Various dynamical behaviors are analysed using the numerical simulations and circuit verifications.     

Weak signal detection and adaptive synchronous stability of a novel fifth-order memristive circuit system

This paper is devoted to introduce a novel complex fifth-order memristive circuit system and its applications in synchronous stability and weak signal detection. Firstly, the typical dynamical behaviors of the memristive system are discussed by chaotic phase portrait, complexity analysis, one-parameter bifurcation and Lyapunov exponent spectrum. Secondly, the adaptive control method is applied to realize the synchronization between the drive memristive system (DMS) and the response memristive system (RMS). The results indicate that the synchronization method has strong robustness and anti-interference ability. Thirdly, the weak signal detection of the novel five-dimensional memristive system is realized by using the extreme sensitivity of chaotic system to initial values. Finally, the fifth-order memristive circuit is designed by using basic electronic elements and simulated by Multisim software. And the anti-interference ability and sensitivity of the fifth-order memristive circuit are further verified by adding different weak disturbance signals at different positions of the circuit.     

Coexistence of multiple bifurcation modes in memristive diode-bridge-based canonical Chua’s circuit

Based on a memristive diode bridge cascaded with series resistor and inductor filter, a modified memristive canonical Chua’s circuit is presented in this paper. With the modelling of the memristive circuit, a normalised system model is built. Stability analyses of the equilibrium points are performed and bifurcation behaviours are investigated by numerical simulations and hardware experiments. Most extraordinary in the memristive circuit is that within a parameter region, coexisting phenomenon of multiple bifurcation modes is emerged under six sets of different initial values, resulting in the coexistence of four sets of topologically different and disconnected attractors. These coexisting attractors are easily captured by repeatedly switching on and off the circuit power supplies, which well verify the numerical simulations.     

基于双曲函数的双忆阻器混沌电路多稳态特性分析

基于经典蔡氏混沌振荡电路,引入一种双曲余弦函数的新型磁控忆阻器模型,设计含有两个双曲余弦忆阻器的混沌电路系统,讨论了系统平衡点集面的稳定区间.选择不同的忆阻初始值进行数值仿真,通过分岔图与Lyapunov指数谱研究双曲忆阻混沌系统的多稳态特性.结果表明,含双曲函数的双忆阻混沌电路具有复杂的动力学行为,运动轨迹不仅依赖于电路参数,还受电路的初始状态影响,由此产生了不同拓扑结构的混沌吸引子与不同周期运动的多稳态隐藏吸引子共存现象.     

基于分数阶忆阻器的混沌电路分析与设计

提出了一种新型的分数阶忆阻混沌电路.首先,建立了分数阶忆阻器的数学模型,通过数值仿真验证了分数阶广义忆阻器满足忆阻器的基本特性.然后,将分数阶广义忆阻器与蔡氏振荡电路相结合,建立了一种基于分数阶广义忆阻器的混沌电路模型.通过稳定性理论,对分数阶系统的稳定性进行了分析.为了进一步研究电路参数对系统动态行为的影响,利用相位...     

双忆阻Shinriki振荡器的超级多稳态和反单调性分析

本文通过在Shinriki振荡器中引入一个有源荷控忆阻,并且利用一个含绝对值项的磁控忆阻代替原电路中的串并联二极管回路,提出了一种含双忆阻器的Shinriki振荡器.根据电路拓扑结构图建立了忆阻振荡器的数学模型,开展了振荡器随电路元件参数变化时的共存分岔、周期-混沌状态转移等动力学特性分析.结果表明,双忆阻Shinriki振荡器对忆阻的参数值和初始条件有极大的依赖性,随着忆阻参数值和初始条件在特定域内变化,振荡器将呈现出共存反单调现象、不完全对称行为、超级多稳态等非线性动力学行为.此外,基于FPGA开发板完成了双忆阻Shinriki振荡器的数字电路仿真,在示波器上捕捉实验波形,验证了动力学分析的正确性.     

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。     

忆阻开关混沌电路及其吸引子共存现象研究

为了研究忆阻开关电路的动力学行为,该文提出一种具有多吸引子共存现象的忆阻开关混沌电路。在该电路中存在多吸引子分岔,当系统中发生边界碰撞之后,系统中将产生不同的吸引子共存现象。其中包括单周期极限环与混沌吸引子共存,不同的混沌吸引子共存,对称的2周期极限环共存现象,以及对称的2周期极限环与5周期极限环共存现象等。该文通过相图、分岔图等数值仿真,分析了该电路的动力学行为,并利用PSIM电路仿真验证了其电路的可行性,对开关电路中多吸引子共存现象和混沌应用的研究具有重要意义。     

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。     

局部有源忆阻器电路及其在HR耦合神经元网络中的应用

该文提出一种新型局部有源忆阻器,使用标准非线性理论分析方法分析其特性,并通过直流伏安特性曲线来证明其局部有源性。此外,将局部有源忆阻器用于模拟生物突触,构建了一个局部有源忆阻突触耦合HR神经元网络。理论分析和数值仿真表明,在局部有源忆阻突触的影响下它能够产生多种放电模式和复杂的混沌行为。最后,实现了该局部有源忆阻突触耦合神经网络的模拟等效电路,并由功率模拟(PSIM)电路仿真验证了数值仿真的正确性。     

Electro-thermal chaotic oscillations of paralleled bipolar transistors

In this work a detailed theoretical analysis of the parallel connection of two power Bipolar Junction Transistors (BJTs), including the self-heating effect, is presented. The analysis of the resulting third-order dynamic system reveals the possibility of inducing chaotic oscillations for suited choices of electrical parameters. The conditions determined by the theoretical analysis are confirmed by numerical simulations of the circuit with parameters reasonable for commercial BJTs.     

新型忆阻器混沌电路及其在图像加密中的应用

忆阻器是一种拥有记忆功能的电阻,目前忆阻器的研究热点及难点在于新模型的建立以及相关方面的应用。该文提出一种基于双曲正弦函数的新型磁控忆阻器模型,通过分析电压和电流的相轨迹关系,发现其具有典型的忆阻器电压-电流特性曲线。利用新建的忆阻器模型构造新型忆阻混沌系统,通过数值仿真绘出新系统的相轨迹图、分岔图、Lyapunov 指数谱等,分析了不同参数时系统的混沌演化过程。另外,基于电路仿真软件Multisim研制了实验仿真电路, 该电路结构简单、易于实际制作,且仿真实验与理论分析结论十分吻合,证实了提出的忆阻混沌系统电路在物理上是可以实现的。最后,利用新系统混沌序列对图像进行加密,重点分析了加密直方图、相邻像素相关性以及抗攻击能力与密钥敏感性,结果表明新系统对图像密钥及明文都非常敏感,密钥空间较大,新提出的忆阻混沌系统应用于图像加密具有较高的安全性能。     

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.     

基于FPGA技术的双磁控忆阻Shinriki振荡器对称行为分析

该文通过将无源磁控忆阻器替换Shinriki振荡器中的二极管串并联支路,并利用有源磁控忆阻代替RLC谐振回路中的电阻,同时在电感支路串联电阻,得到一个新型双磁控忆阻Shinriki振荡器。通过特定参数的共存分岔图和Lyapunov指数谱,开创性地发现了振荡器具有的对称分岔行为,在双参数平面内展现运动状态分布的对称性。同时,在对称参数-初值平面的吸引盆中,分析对称域内系统的多稳态特性。并对存在的对称反单调现象、多运动状态吸引子对称共存和对称域中依赖初值的不完全对称行为进行研究。此外,基于FPGA技术完成双磁控忆阻Shinriki振荡器的数字电路实验,示波器上捕捉的波形验证了系统对称动力学行为分析的正确性。     

基于双曲正切忆阻器的Duffing系统中簇发、共存分析及其DSP实现

忆阻器作为第4种基本电路元件由蔡少棠首次提出,它的提出为混沌电路的设计和工程应用提供了新思路。该文通过在Homles型Duffing系统中引入一个双曲正切忆阻模型,得到了一个新忆阻Duffing非自治系统。利用转换相图、相图、Lyapunov指数等,揭示了该系统具有振荡尖峰数目可控簇发、非完全对称双边簇发、非完全对称的簇发共存、多种周期混沌共存等新颖动力学行为。并通过分岔图及平衡点分析,研究了其簇发产生机理。采用Multisim电路仿真与数字信号处理平台(DSP)对系统进行了硬件实现,与理论分析基本一致的实验结果证明该系统是可行的且是物理可实现的。     

Memristive devices and systems

A broad generalization of memristors--a recently postulated circuit element--to an interesting class of nonlinear dynamical systems called memristive systems is introduced. These systems are unconventional in the sense that while they behave like resistive devices, they can be endowed with a rather exotic variety of dynamic characteristics. While possessing memory and exhibiting small-signal inductive or capacitive effects, they are incapable of energy discharge and they introduce no phase shift between the input and output waveforms. This zero-crossing property gives rise to a Lissajous figure which always passes through the origin. Memristive systems are hysteretic in the sense that their Lissajous figures vary with the excitation frequency. At very low frequencies, memristive systems are indistinguishable from nonlinear resistors while at extremely high frequencies, they reduce to linear resistors. These anomalous properties have misled and prevented the identification of many memristive devices and systems-including the thermistor, the Hodgkin-Huxley membrane circuit model, and the discharge tubes. Generic properties of memristive systems are derived and a canonic dynamical system model is presented along with an explicit algorithm for identifying the model parameters and functions.     

分数阶忆阻退化Jerk系统的特性分析与DSP实现

为了探究分数阶形式下该类系统的动力学特性,该文将分数阶微积分引入到忆阻退化Jerk系统中,增加了一个自由度,提升了系统性能。通过相图、分岔图、李雅普诺夫指数谱、复杂度混沌图等分析了系统的动力学特性,并采用DSP技术,实现了该系统的数字电路。研究结果表明,系统拓展到分数阶后有两种不同的单涡卷吸引子,系统随初值变化呈现倍周期分岔路径,在某些特定初值处系统演化路径出现跃变。系统具有无限多个吸引子共存。     

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.     

忆阻高通滤波电路准周期与混沌环面簇发振荡及慢通道效应

该文提出了一种忆阻高通滤波电路,它是由有源高通RC滤波器与二极管桥级联LC振荡器的忆阻模拟器并联耦合组成的。该文建立了电路方程与系统模型。基于分岔图、相平面图、庞加莱映射等数值仿真,开展了以反馈增益为可调参数的分岔分析,揭示了忆阻高通滤波电路中存在的准周期、混沌环面、混沌和多周期等簇发振荡行为。进一步地,通过快慢分析法,导出了快子系统的Hopf分岔集,并进而阐述了忆阻高通滤波电路慢通道效应的形成机理。最后,基于Multisim电路仿真验证了数值仿真结果。     

非对称忆阻诱导的吸引子非对称演化与机理研究

紧磁滞回线是评测物理器件或数学模型是否为忆阻的关键依据,其对称特性也是忆阻的重要特征之一。该文提出一种有源非对称忆阻二极管桥模拟器,它通过改变二极管桥中并联二极管的数量可实现紧磁滞回线非对称度的控制。首先,验证了该非对称忆阻模拟器的指纹特征,并着重探讨了激励频率和对称度控制参数对紧磁滞回线非对称度的影响。进一步地,将该非对称忆阻模拟器耦合到Sallen-Key高通滤波器,构建了一种无感忆阻蔡氏电路;建立了相应的无量纲系统,并揭示了系统吸引子的非对称演化现象。结合平衡点稳定性分析、分岔分析和多吸引子状态初值空间分布,阐明了吸引子非对称演化的产生机理。结果表明,受非对称忆阻的影响,无感忆阻蔡氏电路的两个不稳定鞍焦点失去平衡,导致了非对称共存分岔、多稳定模态等行为的产生。最后,由硬件电路实验验证了理论分析与数值仿真的正确性。