基于Simulink的Chua’s Circuit混沌实验的可视化模型及仿真研究

以大学物理实验中的Chua’s Circuit混沌实验为例，提出了运用Simulink建立Chua’s Circuit混沌实验可视化模型的方法，并对混沌系统的几种状态进行仿真研究。

A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control

Dynamical variables of coupled nonlinear oscillators can exhibit different synchronization patterns depending on the designed coupling scheme. In this paper, a non-fragile linear feedback control strategy with multiplicative controller gain uncertainties is proposed for realizing the mixed-synchronization of Chua＇s circuits connected in a drive-response configuration. In particular, in the mixed-synchronization regime, different state variables of the response system can evolve into complete synchronization, anti-synchronization and even amplitude death simultaneously with the drive variables for an appropriate choice of scaling matrix. Using Lyapunov stability theory, we derive some sufficient criteria for achieving global mixed-synchronization. It is shown that the desired non-fragile state feedback controller can be constructed by solving a set of linear matrix inequalities （LMIs）. Numerical simulations are also provided to demonstrate the effectiveness of the proposed control approach.

Synchronising chaotic Chua's circuit using switching feedback control based on piecewise quadratic Lyapunov functions

This paper investigates the chaos synchronisation between two coupled chaotic Chua＇s circuits. The sufficient condition presented by linear matrix inequalities （LMIs） of global asymptotic synchronisation is attained based on piecewise quadratic Lyapunov functions. First, we obtain the piecewise linear differential inclusions （pwLDIs） model of synchronisation error dynamics, then we design a switching （piecewise-linear） feedback control law to stabilise it based on the piecewise quadratic Laypunov functions. Then we give some numerical simulations to demonstrate the effectiveness of our theoretical results.

Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

Chua＇s circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua＇s circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the su- percritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous （PWSC） systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. There- fore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.

DESIGN METHOD OF CHUA'S CIRCUIT FOR SPECIFIED SPECTRUM DISTRIBUTION

Based on the α-β bifurcation curves and the special characteristics of chaotic spectrum of chua’s circuit, this paper presents here a method for designing a Chua’s circuit which approximately satisfy specified spectrum distribution range.

Chaotic behavior learning of Chua's circuit

Least-square support vector machines（LS-SVM） are applied for learning the chaotic behavior of Chua＇s circuit.The system is divided into three multiple-input single-output（MISO） structures and the LS-SVM are trained individually.Comparing with classical approaches,the proposed one reduces the structural complexity and the selection of parameters is avoided.Some parameters of the attractor are used to compare the chaotic behavior of the reconstructed and the original systems for model validation.Results show that the LS-SVM combined with the MISO can be trained to identify the underlying link among Chua＇s circuit state variables,and exhibit the chaotic attractors under the autonomous working mode.

Study on eigenvalue space of hyperchaotic canonical four-dimensional Chua's circuit

The eigenvalue space of the canonical four-dimensional Chua＇s circuit which can realize every eigenvalue for fourdimensional system is studied in this paper. First, the analytical relations between the circuit parameters and the eigenvalues of the system are established, and therefore all the circuit parameters can be determined explicitly by any given set of eigenvalues. Then, the eigenvalue space of the circuit is investigated in two cases by the nonlinear elements used. According to the types of the eigenvalues, some novel hyperchaotic attractors are presented. Further, the dynamic behaviours of the circuit are studied by the bifurcation diagrams and the Lyapunov spectra of the eigenvalues.

Controllability of fractional-order Chua's circuit

The ultimate proof of our understanding of nature and engineering systems is reflected in our ability to control them.Since fractional calculus is more universal, we bring attention to the controllability of fractional order systems. First,we extend the conventional controllability theorem to the fractional domain. Strictly mathematical analysis and proof are presented. Because Chua＇s circuit is a typical representative of nonlinear circuits, we study the controllability of the fractional order Chua＇s circuit in detail using the presented theorem. Numerical simulations and theoretical analysis are both presented, which are in agreement with each other.

The Modifications of Wagner’s Equation and Electrochemistry for the 21st Century

The use of samarium-doped ceria (SDC) electrolytes in SOFCs (solid oxide fuel cells) lowers the open circuit voltage (OCV) below the Nernst voltage (Vth). The OCV is calculated with Wagner’s equation which is included in NernstPlanck equation. Considering the separation of Boltzmann distribution, the fundamental basis of this topic is discussed. A constant voltage loss without leakage currents due to a mixed ionic and electronic conducting (MIEC) dense anode was explained. Only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, which is determined by incorporating a different constant in the definitions of chemical potential and electrical potential. This difference explains the results using dense MIEC anodes. This topic is not an isolated and minor topic, but of vital importance to electrochemical engineering for the 21st Century.

基于Multisim四阶蔡氏电路混沌保密通信系统仿真分析

利用Multisim软件构建四阶蔡氏电路混沌保密通信仿真电路,利用驱动-响应同步法实现收发系统的同步,利用混沌掩盖方案对信息信号进行掩盖,实现对信息信号保密的目的。仿真结果表明,此系统可以实现保密通信。

基于蔡氏电路和DES的图像加密算法

针对Data Encryption Standard(DES,数据加密标准)算法所存在的不足和混沌序列的特点,提出了一种新的基于蔡氏电路和DES的图像加密算法。该算法将蔡氏电路所生成的混沌序列与DES算法相结合,对加密时所用的初始密钥和16轮迭代运算过程进行了改进。把混沌加密技术嵌入到迭代运算过程中,理论分析和实验仿真结果表明,与DES算法相比,该算法扩展了初始密钥选择空间,有效地提高了算法安全性能和抵抗攻击能力。新算法更利于图像信息传递,同时更好地保证了信息的安全性和保密性。

Chua电路分析平台的设计

针对目前研究Chua混沌电路各环节的不直观性和计算电路参数的复杂性,设计了一个用户平台,可对Chua混沌电路的参数、初始条件、特征值、矢量场、运动轨迹等各个环节进行全面、直观的反映.实例验证了该平台对分析Chua混沌电路有全面、准确、方便等特性,可进一步方便地研究电路.因此该平台具有极强的应用与推广价值.

基于T-S模糊模型的蔡氏混沌电路及其输出反馈同步

针对蔡氏混沌电路,研究其T-S模糊模型及其输出反馈同步问题。根据蔡氏混沌电路非线性项的特点,选择合适的前件变量、隶属度函数和模糊规则,得到与原来蔡氏混沌电路完全等价的T-S模糊模型。在此模型的基础上,设计输出反馈控制器,利用Lyapunov稳定性理论和线性矩阵不等式,给出蔡氏混沌电路输出反馈同步控制参数。最后通过数值仿真,验证控制器的有效性。

Describing Chaos of Continuous Time System Using Bounded Space Curve

The qualitative solutions of dynamical system expressed with nonlinear differential equation can be divided into two categories. One is that the motion of phase point may approach infinite or stable equilibrium point eventually. Neither periodic excited source nor self-excited oscillation exists in such nonlinear dynamic circuits, so its solution cannot be treated as the synthesis of multiharmonic. And the other is that the endless vibration of phase point is limited within certain range, moreover possesses character of sustained oscillation, namely the bounded nonlinear oscillation. It can persistently and repeatedly vibration after dynamic variable entering into steady state;moreover the motion of phase point will not approach infinite at last;system has not stable equilibrium point. The motional trajectory can be described by a bounded space curve. So far, the curve cannot be represented by concretely explicit parametric form in math. It cannot be expressed analytically by human. The chaos is a most universally common form of bounded nonlinear oscillation. A number of chaotic systems, such as Lorenz equation, Chua’s circuit and lossless system in modern times are some examples among thousands of chaotic equations. In this work, basic properties related to the bounded space curve will be comprehensively summarized by analyzing these examples.

一种改进型蔡氏电路的PSPICE仿真研究

介绍了一种四阶改进型蔡氏电路。首先建立了电路的数学模型,通过PSPICE软件研究了改进电路的混沌特性,然后采用驱动响应法实现了电路的混沌同步,最后通过仿真实验实现了此电路在保密通信中的应用。结论证明此电路产生的混沌信号比原蔡氏电路更加复杂,且通过改变RC并联电路参数即可很容易得到不同的混沌信号,因而更适用于混沌保密通信。

Adaptive fuzzy controller for a class of strict-feedback nonaffine nonlinear systems

A robust adaptive fuzzy control scheme is presented for a class of strict-feedback nonaffine nonlinear systems with modeling uncertainties and external disturbances by using a backstepping approach.Fuzzy logic systems are employed to approximate the unknown parts of the desired virtual controls,and the approximation errors of fuzzy systems are only required to be norm-bounded.The function tanh（·） is introduced to avoid problems associated with sgn（·）.The tracking error is guaranteed to be uniformly ultimately bounded with the aid of an additional adaptive compensation term.Chua＇s circuit system and R o¨ssler system are presented to illustrate the feasibility and effectiveness of the proposed control technique.

一个光滑Chua系统的同步问题研究

主要考虑光滑Chua系统的自同步,分别采用反馈同步法和自适应同步法对光滑Chua系统进行同步控制,并借助计算机技术通过数值模拟验证了理论方法的有效性和正确性。

Impulsive stabilization of a class of nonlinear system with bounded gain error

Considering mechanical limitation or device restriction in practical application, this paper investigates impulsive stabilization of nonlinear systems with impulsive gain error. Compared with the existing impulsive analytical approaches,the proposed impulsive control method is more practically applicable, which includes control gain error with an acceptable boundary. A sufficient criterion for global exponential stability of an impulsive control system is derived, which relaxes the condition for precise impulsive gain efficiently. The effectiveness of the proposed method is confirmed by theoretical analysis and numerical simulation based on Chua＇s circuit.

Electromagnetic Interpretation of Fractional-Order Elements

Fractional circuits have attracted extensive attention of scholars and researchers for their superior performance and potential applications. Recently, the fundamentals of the conventional circuit theory were extended to include the new generalized elements and fractional-order elements. As is known to all, circuit theory is a limiting special case of electromagnetic field theory and the characterization of classical circuit elements can be given an elegant electromagnetic interpretation. In this paper, considering fractional-order time derivatives, an electromagnetic field interpretation of fractional-order elements: fractional-order inductor, fractional-order capacitor and fractional-order mutual inductor is presented, in terms of a quasi-static expansion of the fractional Maxwell’s equations. It shows that fractional-order elements can also be interpreted as a fractional electromagnetic system. As the element order equals to 1, the interpretation of fractional-order elements matches that of the classical circuit elements: L, C, and mutual inductor, respectively.

一类无感蔡氏电路的综合设计性实验

为服务于本科院校电子信息类专业课程的综合设计性实验需求,设计了一类无感蔡氏电路。无感蔡氏电路采用模块化设计思路,提供了三类蔡氏二极管等效电路和四类二阶有源RC滤波器,以满足多样化设计需求。通过具体案例,展示了无感蔡氏电路的数学建模、数值仿真、电路仿真、电路设计与硬件实验的完整过程,可作为“电子技术课程设计”“电子综合实训”等课程的教学范例。