Adaptive synchronization of memristor-based Chuaʼs circuits

In this Letter, a memristor-based Chua?s system is presented, and the chaotic behavior of this system is demonstrated by phase portraits. This Letter also deals with the problem of adaptive synchronization control of this chaotic system using the drive–response concept, and presents an adaptive control scheme for the synchronization of memristor-based Chua?s circuit, when the parameters of the drive system are fully unknown and different with those of the response system. The sufficient condition for the adaptive synchronization has been analyzed. Moreover, the controller design method is further extended to more general cases, where the physical plant contains parameter uncertainties, represented in either polytopic or structured frameworks. Numerical simulations are used to demonstrate these results.     

Localization of hidden Chua?s attractors

The classical attractors of Lorenz, Rossler, Chua, Chen, and other widely-known attractors are those excited from unstable equilibria. From computational point of view this allows one to use numerical method, in which after transient process a trajectory, started from a point of unstable manifold in the neighborhood of equilibrium, reaches an attractor and identifies it. However there are attractors of another type: hidden attractors, a basin of attraction of which does not contain neighborhoods of equilibria. In the present Letter for localization of hidden attractors of Chua?s circuit it is suggested to use a special analytical-numerical algorithm.     

五阶压控忆阻蔡氏混沌电路的双稳定性

通过在蔡氏电路的耦合电阻支路中串联一个电感,采用压控忆阻替换蔡氏电路中的蔡氏二极管,提出了一种新颖的五阶压控忆阻蔡氏混沌电路.建立该电路的数学模型,从理论上分析了平衡点及其稳定性的演化过程.特别地,该电路在给定参数下只有一个不稳定的零平衡点,却形成了混沌与周期的非对称吸引子共存的吸引盆,意味着双稳定性的存在.进而利用数值仿真与PSIM电路仿真着重研究了本文电路在不同初始状态下产生的双稳定性现象及其形成机理.PSIM电路仿真结果与数值仿真结果一致,较好地验证了理论分析.借助分岔图、李雅普诺夫指数、相轨图和吸引盆进一步深入探讨了归一化五阶压控忆阻蔡氏系统依赖于系统初始条件的动力学行为.结果表明,该忆阻蔡氏系统在不同的初始条件下能够呈现出混沌吸引子与周期极限环共存的双稳定性现象.     

Synchronization,circuit and secure communication implementation of a memristor-based hyperchaotic system using single input controller

In this paper, we investigate a circuit implementation of memristor-based chaotic synchronization with a single input controller. Firstly, based on the cubic function model of memristor, a circuit with the grounded flux-control memristor-based hyperchaotic system is designed and implemented. Secondly, a single input controller is proposed to synchronize the two memristor-based hyperchaotic systems, and a sufficient condition of the synchronized system is obtained by the Routh-Hurwitz criterion and minimum phase theory. Then, a circuit of the proposed controller for memristor-based chaotic synchronization system is designed and implemented. Finally, secure communication based on memristor-based chaotic synchronization system is given to show the feasibility of the signal encryption scheme.     

基于模糊观测器的Chua混沌系统投影同步

研究了Chua混沌系统的广义投影同步问题.基于Takagi-Sugeno(T-S)模糊模型,设计了一种模糊观测器.利用Lyapunov稳定性理论证明了所提方案的可行性和全局稳定性.数值仿真试验进一步验证了该方案可以实现Chua混沌系统的投影同步.方法设计简单,且可以推广到其他的一些混沌系统. 关键词： T-S模糊模型 Chua混沌系统 观测器 投影同步     

Experimental observation of direct current voltage-induced phase synchronization

The dynamics of two uncoupled distinct Chua circuits driven by a common direct current voltage is explored experimentally. It was found that, with increasing current intensity, the dominant frequencies of these two Chua circuits will first vary at different speeds, approach an identical value for a certain current intensity and then separate. Techniques such as synchronization index and phase difference distribution were employed to analyze the phase coherence between these two Chua circuits.     

Design of a memcapacitor emulator based on a memristor

Since Hewlett-Packard?s solid state implementation of a memristive system in 2008, a lot of research has begun to develop applications using this new component. As it is not available as a two terminal device yet, emulating circuits must be developed. Building on our previous work to develop an analog model of a memristor, a memcapacitor emulator is proposed in this Letter. This model can be realized by transforming a memristor emulator to a memcapacitor emulator. The characteristics of a memcapacitor are based on the theory proposed by L.O. Chua. The transformation process is described in detail in this Letter. Simulation and experimental results are given as well.     

Stability criterion for projective synchronization in three-dimensional chaotic systems

Projective synchronization, in which the state vectors synchronize up to a scaling factor, has recently been observed in coupled partially linear chaotic systems (Lorenz system) under certain conditions. In this Letter, we present a stability criterion that guarantees the occurrence of the projective synchronization in three-dimensional systems. By applying the criterion to two typical partially linear systems (Lorenz and disk dynamo), it shows that only some parameters play the key role in influencing the stability. Projective synchronization only happens when σ>−1 for the Lorenz and μ>0 for the disk dynamo.     

Adaptive fuzzy bilinear observer based synchronization design for generalized Lorenz system

This Letter proposes an adaptive fuzzy bilinear observer (FBO) based synchronization design for generalized Lorenz system (GLS). The GLS can be described to TS fuzzy bilinear generalized Lorenz model (FBGLM) with their states immeasurable and their parameters unknown. We design an adaptive FBO based on TS FBGLM for synchronization. Lyapunov theory is employed to guarantee the stability of error dynamic system via linear matrix equalities (LMIs) and to derive the adaptive laws to estimate unknown parameters. Numerical example is given to demonstrate the validity of our proposed adaptive FBO approach for synchronization.     

Projective synchronization of a new hyperchaotic Lorenz system

This Letter mainly concerns projective synchronization (PS) of a new hyperchaotic Lorenz system. PS with both identical and different scaling factors between two hyperchaotic Lorenz systems are realized. A general sufficient condition for PS in a certain class of chaotic (hyperchaotic) system with uncertainties is obtained by using adaptive control. Numerical simulations are performed to verify and illustrate the analytical results.     

具有非线性控制的Chua电路的混沌同步

Chua电路是一个非光滑系统.本文通过广义哈密顿系统和观测器方法,将具有非线性控制的Chua电路的混沌同步问题转化成研究具有非线性控制的光滑系统的零解稳定性;进而利用滑模控制对该光滑系统的零解稳定性进行了研究,从而使得Chua电路达到了混沌同步.最后,将上述方法应用到具体系统,数值结果也表明其正确性.     

基于线性反馈控制的不确定混沌系统的参数辨识

基于线性反馈控制方法和Lyapunov稳定性理论,研究了参数不确定系统的混沌同步和参数辨识,设计了普遍适用的参数自适应控制律,理论证明设计的控制器可使得两个结构相同但参数不同的混沌系统渐近地达到同步,并且可以辨识出响应系统的未知参数. Lorenz系统和蔡氏电路的数值仿真进一步表明了该方法的有效性. 关键词： 不确定混沌系统 同步 参数辨识 Lyapunov函数     

How similar is the performance of the cubic and the piecewise-linear circuits of Chua?

This Letter reports phase diagrams quantifying and contrasting the dynamical performance of the paradigmatic piecewise-linear and cubic circuits of Chua. Although both circuits may be regarded as macroscopically isomorphic over wide regions in control parameter space, we show that their microscopic structure displays a myriad of rather distinctive intrinsic features making them unique. Inhomogeneities embedded in periodic and chaotic phases complicate some applications of the circuits but may also adequately act as realistic noise proxies in synchronization problems. In addition, infinite cascades of spirals and hubs observed experimentally very recently in a related dissipative flow are shown to be also present in both circuits of Chua, emerging however in a rather distinctive asymmetric way. Thus Chua's circuits may be used to study experimentally elusive and theoretically intricate phenomena generating periodicity hubs.     

忆阻混沌系统的脉冲同步与初值影响研究

以光滑三次型磁控忆阻器的蔡氏电路为例, 研究了两个同构忆阻混沌系统的脉冲控制同步方法.基于Lyapunov稳定性理论, 给出了忆阻混沌系统的脉冲同步渐近稳定条件; 结合误差系统的最大条件Lyapunov指数谱, 讨论了系统初值对脉冲同步性能的影响, 并进行了相应的数值仿真实验.结果表明, 在合适的脉冲控制参数条件下, 同构的忆阻混沌系统的脉冲同步是可行而有效的; 忆阻混沌系统的初值对脉冲同步性能存在一定的影响, 但可通过增大脉冲耦合强度来抑制系统初值的影响.     

一种二次型忆阻器四阶混沌电路

由HP实验室研制的无源忆阻器得到的荷控二次型忆阻器模型,与有源磁控分段线性和三次光滑忆阻器模型相比,更符合实际.利用此模型并基于蔡氏混沌电路演化而来的拓扑对偶结构设计了一种新型忆阻器四阶混沌电路.理论分析、仿真及电路实现表明,该电路具有依赖于忆阻器初始状态的复杂动力学行为,也会产生随时间和系统参数变化的状态转移等非线性动力学现象,在相轨图中出现"涡眼"和"环眼".     

Double compound combination synchronization among eight n-dimensional chaotic systems

Depending on double compound synchronization and compound combination synchronization, a new kind of synchronization is introduced which is the double compound combination synchronization(DCCS) of eight n-dimensional chaotic systems. This kind may be considered as a generalization of many types of synchronization. In the communication, based on many of drive and response systems, the transmitted and received signals will be more secure. Using the Lyapunov stability theory and nonlinear feedback control, analytical formulas of control functions are obtained to insure our results. The corresponding analytical expression and numerical treatment are used to show the validity and feasibility of our proposed synchronization scheme. The eight memristor-based Chua oscillators are considered as an example. Other examples can be similarly investigated. The proposed synchronization technique is supported using the MATLAB simulation outcomes. We obtain the same results of numerical treatment of our synchronization using simulation observations of our example.     

Mapping equivalent approach to analysis and realization of memristor-based dynamical circuit

A novel mapping equivalent approach is proposed in this paper, which can be used for analyzing and realizing a memristor-based dynamical circuit equivalently by a nonlinear dynamical circuit with the same topologies and circuit parameters. A memristor-based chaotic circuit and the corresponding Chua’s chaotic circuit with two output differentiators are taken as examples to illustrate this approach. Equivalent dynamical analysis and realization of the memristor-based chaotic circuit are performed by using Chua’s chaotic circuit. The results indicate that the outputs of memristor-based chaotic circuit and the corresponding outputs of Chua’s chaotic circuit have identical dynamics. The proposed approach verified by numerical simulations and experimental observations is useful in designing and analyzing memristor-based dynamical circuits.     

利用周期信号驱动Chua电路实现相同步

我们在实验上和理论上对周期信号驱动的混沌电路的相同步问题进行了研究。我们选择三类周期信号作为驱动信号，包括Chua电路产生的周期信号，正弦信号和脉冲信号。改变驱动信号的频率、振幅和脉冲信号的占空比，在周期信号和混沌信号存在小的频率失配的条件下，驱动信号的振幅在适当的变化范围内，以及脉冲信号的占空比在适当的变化范围内，都可以获得相同步。甚至当占空比小到3%的情况下，仍然可以得到相同步。特别是这类脉冲信号的控制在实际中是有意义的。     

蔡氏电路的功能全同电路与拓扑等效电路及其设计方法

基于经典蔡氏电路方程的电容电压与电感电流变量及其状态方程归一化特点,提出了三种标度化、优化的电路设计方法:一种是方程变量都为电压的5运放电源限幅蔡氏电路,便于大规模集成;两种二极管非线性构成的功能全同蔡氏电路,与限幅非线性电路优势互补,可供大规模集成的细胞神经网络系统设计;同时,给出了与蔡氏电路为微分同胚电路的优化三次方蔡氏电路.各电路设计方法适用于以三折线为主的三次型混沌电路.最后,将本文提出的电路设计方法应用于混沌保密通信,实验表明该方法具有实用性和一定的应用价值.