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.

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。

Synchronization of Modified Chua＇s Circuit with x｜x｜ Function

This paper considers the chaos synchronization of the modified Chua 's circuit with x|x| function. We firstly show that a couple of the modified Chua systems with different parameters and initial conditions can be synchronized using active control when the values of parameters both in drive system and response system are known aforehand.Furthermore, based on Lyapunov stability theory we propose an adaptive active control approach to make the states of two identical Chua systems with unknown constant parameters asymptotically synchronized. Moreover the designed controller is independent of those unknown parameters. Numerical simulations are given to validate the proposed synchronization approach.

Science Letters:The Moore’s Law for photonic integrated circuits

We formulate a “Moore’s law” for photonic integrated circuits (PICs) and their spatial integration density using two methods. One is decomposing the integrated photonics devices of diverse types into equivalent basic elements, which makes a comparison with the generic elements of electronic integrated circuits more meaningful. The other is making a complex compo- nent equivalent to a series of basic elements of the same functionality, which is used to calculate the integration density for func- tional components realized with different structures. The results serve as a benchmark of the evolution of PICs and we can con- clude that the density of integration measured in this way roughly increases by a factor of 2 per year. The prospects for a continued increase of spatial integration density are discussed.

Analytical Criteria for Local Activity of CNN with Two Ports and Application to Smoothed Chua's Circuit

Presents analytic criteria for the local activity theory in two-port cellularneural network (CNN) cells with four local state variables, and gives the application to a smoothedChua's circuit (SCC) CNN with two-port and I 5 S 15 arrays. The bifurcation diagrams of the SCC CNNshow that they are completely the same as those of an SCC CNN with one-port calculated earlier;which do not exist locally passive domain. The evolution of the patterns of the state variables ofthe SCC CNN is stimulated. Oscillatory patterns, chaotic patterns, or divergent patterns may emergeif the selected cell parameters are located in the locally active unstable domains but nearby theedge of chaos domain.

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.

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.

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.

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.

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.

Analytical criteria for local activity of CNN with five state variables and application to Hyper-chaos synchronization Chua's circuit

The analytic criteria for the local activity theory in one-port cellularneural network (CNN) with five local state variables are presented. The application to a Hyper-chaossynchronization Chua's circuit (HCSCC) CNN with 1125 variables is studied. The bifurcation diagramsof the HCSCC CNN show that they are slightly different from the smoothed CNN with one or two portsand four state variables calculated earlier. The evolution of the patterns of the state variables ofthe HCSCC CNN is stimulated. Oscillatory patterns, chaotic patterns, convergent or divergentpatterns may emerge if the selected cell parameters are located in the locally active domains butnearby or in the edge of chaos domain.

A RANDOM SEQUENCE GENERATOR BASED ON CHAOTIC CIRCUITS

In this paper, a random sequence generator based on chaotic circuits is presented.Fundamental principle and experimental circuit have been carried out in case of Chua's circuit.The statistical results are in good agreement with probability characteristics of random sequence.

Filling the Teaching Gap between Electromagnetics and Circuits

Electrical engineers normally are taught electromagnetism in an electromagnetics course （e.g. in [ 1-2]）, and circuit analysis in an independent course （e.g. in [4-6]）. Circuits are dominated by Kirchhoff s laws, while electromagnetics is dominated by Maxwell＇s equations. However, the correspondence between two sets of equations is not immediately perceived and this creates some uncertainty in the young electrical or electronic engineer, which may grow with the doubt that KirchhotTs laws may be somewhat laws of the nature independent of the laws of electromagnetism. This paper has the purpose of supplying teaching material that may be used to fill the gap, and therefore be taught either at the end of an electromagnetics or at the beginning of a circuit course. It exploits large parts of the paper published in a conference [8], but also contains significant enhancements. The paper first shows simple distributed parameter systems, whose behaviour follows Maxwell＇s equations, and then shows that they, under given assumptions, can be modelled as circuits, whose behaviour is governed by Kirchhoff＇s laws.

A Comparative Study of Analytical Solutions to the Coupled Van-der-Pol’s Non-linear Circuits Using the He’s Method(HPEM)and(BPES)

In this paper, the He’s parameter-expanding method (HPEM) and the 4q-Boubaker Polynomials Expansion Scheme (BPES) are used in order to obtain analytical solutions to the non-linear modified Van der Pol’s oscillating circuit equation. The resolution protocols are applied to the ordinary Van der Pol equation, which annexed to conjoint delayed feedback and delay-related damping terms. The results are plotted, and compared with exact solutions proposed elsewhere, in order to evaluate accuracy.

Chair's Introduction to 2009 IEEE Circuits and Systems International Conference on Testing and Diagnosis

Based on the recommendation of ICTD＇09 TPC members, this Special Issue of the Journal of Electronic Science ＆ Technology of China （JESTC） contained 22 high quality papers selected from the Proceedings of 2009 IEEE Circuits and Systems International Conference on Testing and Diagnosis （ICTD ＇09） which is fully sponsored by the IEEE Circuits and Systems Society （CASS）, and is technically co-sponsored by the University of Electronic Science and Technology of China （UESTC）, the Chinese Institute of Electronics （CIE）, the China Instrument ＆ Control Society （CIS）, and organized by UESTC.

Chua’s系统的追踪控制与同步

为对Chua’s混沌系统进行控制,设计出一种含参控制器,使得受控系统的某一状态变量能追踪任意给定的参考信号,利用Lyapunov函数方法证明在此控制器作用下,该系统的状态变量按指数速率收敛到参考信号。在此基础上,研究受控Chua’s混沌系统的自同步和异结构同步问题,数值仿真结果说明了此控制器设计方法的有效性。

一类非光滑Chua's电路的同步控制

本文研究两个带x|x|非线性项的Chua's电路的全局指数同步和全局同步的控制问题.证明这两个系统在未加控制时不可能同步,但设计不同的控制器可以实现这两个系统的全局指数同步和全局同步.

一类光滑Chua's电路的自适应同步

讨论了一种变形的光滑Chua's电路的自适应同步控制问题.当从动系统对主动系统的参数未知时,采用Lyapunov稳定性理论和自适应设计方法,设计出一个自适应控制器.通过该控制器,实现了主从系统间的自适应同步.仿真结果表明该设计方法是有效的.

一类光滑Chua’s电路的Lagrange稳定性分析

本文讨论了一类Chua’s电路的Lagrange稳定性.首先从理论上证明了该系统具有全局指数吸引域和正向不变集.通过设计适当的线性控制器,实现了平衡点的指数稳定性和周期解的指数跟踪.数值仿真验证的控制策略的有效性.