Input and output coupled nonlinear systems

In this paper, a class of input and output coupled nonlinear systems with multiple equilibria are studied. These kinds of systems can also be viewed as interconnected systems composed of single-input and single-output systems through some linear and nonlinear interconnections. Frequency-domain conditions are established for global convergence and convergence of bounded solutions for such systems. The effects of nonlinear input and output interconnections can be studied through a nonsingular matrix. The design method based on linear matrix inequality for the interconnected matrix is presented. In addition, the relation between input and output coupling here and input transformation in control theory is established. The coupling method is illustrated through a coupled Chua's circuit. The nonexistence of chaotic attractors or limit cycles in the coupled Chua's circuit can be analyzed by convergence of bounded solutions.     

Interaction of Capacitive and Resistive Nonlinearities in Chua's Circuit

The interaction of capacitive and resistivenonlinearities in the Chua's circuit is studied.The original Chua's circuit is modified by replacing one of thelinear capacitors with a nonlinear one to investigate the effectsof such an interaction on the chaotic behavior of the circuit.It is found that such an interaction can be effective in limitingand controlling chaos. The Pspice simulation results are alsogiven and compared with our numerical solutions.     

混沌系统同步的抗干扰优化设计

本文研究混沌系统同步的抗信道噪声和参数失配干扰优化设计问题。以非线性反馈混沌同步方案为基础，推导出一种抗干扰优化设计方法。对蔡氏电路的仿真实验表明，用该方法设计的混沌同步系统具有较强的抗干扰能力。     

存在参数微扰的非自治超混沌系统的同步

本文对四维非自治的超混沌光学模型的同步问题进行了讨论。结合误差反馈同步方法和参数自适应同步方法,使参数不同的两个系统达到同步,数值计算结果也表明同步效果很好。同时对控制函数的参数与同步建立的时间两者之间的关系进行了仿真,结果表明,存在最佳参数使得同步建立的时间最短。     

混沌系统的反相延迟同步

结合反向同步和延迟同步,提出一种新颖的反相延迟同步,基于状态观测器构造响应系统,并利用极点配置技术得到误差系统在原点处渐近稳定,实现了反相延迟同步.用Chen's混沌系统和Chua's电路为例进行数值仿真,在预先设定特征值的基础上,经极点配置可得到同步的响应系统,实验结果显示该方案简单有效.     

Robust Dichotomy Analysis and Synthesis With Application to an Extended Chua's Circuit

Dichotomy, or monostability, is one of the most important properties of nonlinear dynamic systems. For a dichotomous system, the solution of the system is either unbounded or convergent to a certain equilibrium, thus periodic or chaotic states cannot exist in the system. In this paper, a new methodology for the analysis of dichotomy of a class of nonlinear systems is proposed, and a linear matrix inequality (LMI)-based criterion is derived. The results are then extended to uncertain systems with real convex polytopic uncertainties in the linear part, and the LMI representation for robust dichotomy allows the use of parameter-dependent Lyapunov function. Based on the results, a dynamic output feedback controller guaranteeing robust dichotomy is designed, and the controller parameters are explicitly expressed by a set of feasible solutions of corresponding linear matrix inequalities. An extended Chua's circuit with two nonlinear resistors is given at the end of the paper to demonstrate the validity and applicability of the proposed approach. It is shown that by investigating the convergence of the bounded oscillating solutions of the system, our results suggests a viable and effective way for chaos control in nonlinear circuits.     

A new chaotic secure communication system

The paper proposes a digital chaotic secure communication by introducing a magnifying glass concept, which is used to enlarge and observe minor parameter mismatch so as to increase the sensitivity of the system. The encryption method is based on a one-time pad encryption scheme, where the random key sequence is replaced by a chaotic sequence generated via a Chua's circuit. We make use of an impulsive control strategy to synchronize two identical chaotic systems embedded in the encryptor and the decryptor, respectively. The lengths of impulsive intervals are piecewise constant and, as a result, the security of the system is further improved. Moreover, with the given parameters of the chaotic system and the impulsive control law, an estimate of the synchronization time is derived. The proposed cryptosystem is shown to be very sensitive to parameter mismatch and hence the security of the chaotic secure communication system is greatly enhanced.     

一种语音混沌保密通信方案的研究与硬件实现

在硬件实验研究的基础上，建立一种环形蔡氏电路，提出用环蔡氏电路实现语音混沌保密通信的一种闭环逆系统方案，其特点是利用环形蔡氏电路的单向耦合原理，通过反馈的方法形成一个包括有用信号在内的极联闭合环路，从而实现改善端与接收端之间混沌系统的严格同步而不受有用信息调制的影响。理论分析与硬件实验结果证明，该方案同现有的其它混沌通信方案相比较，具有非线性失真小、保真度高的优点，完全能够满足传送语音信号的要求。     

Control of Chua's circuit with a cubic nonlinearity via nonlinear linearization technique

This paper addresses the controlling chaos problem of a cubic variant for the original Chua's circuit. A conventional input-output transfer function of a linearized system and a nonlinear linearization technique for a nonlinear system are also presented. According to analytical results, at equilibrium, the notion of local phase-minimality of the nonlinear system is equivalent to that of the linear system's transfer function. Our results also demonstrate that the controlled Chua's circuit, while considering a certain state as the system output, is an input-output linearizable minimum-phase system. In addition, nonlinear control laws are derived such that each state asymptotically tracks its corresponding desired trajectory while maintaining the boundedness of all signals inside the system.     

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.     

蔡氏电路混沌同步保密通讯

两个相同的蔡氏电路(Chua’s Circuit)互相耦合可以实现混沌(Chaos)同步是混沌研究的一个重要成果．也是探索蔡氏电路开发应用的基础。应用蔡氏电路的同步特性实现保密通讯是当前蔡氏电路开发应用研究的一个主要方向。本文在介绍蔡氏电路混沌同步特性的基础上，讨论主—从式蔡氏电路同步保密通讯系统及实现双向通讯和无线传输的可行性．并对这种保密通讯系统的安全性与鲁棒性(Robustness)作了简要的分析.     

混沌电路同步及其在通信中的应用研究

混沌在实际系统中是很常见的，但直到最近工程人员大都把它作一种无用的东西并极力去避免它。本文给出了一个蔡氏电路系统在固有的混沌模式下实现同步的可能性。     

基于混沌同步的混沌脉冲定位调制研究

随着混沌理论和混沌同步的发展及完善，根据混沌脉冲定位调制（CPPM）的基本原理，提出一种基于混沌同步的混沌脉冲定位调制（CS—CPPM）实现方法，建立以蔡氏混沌同步电路和Logstic映射为例的实现模型，用EWB仿真软件对蔡氏二极管、蔡氏电路以及蔡氏同步电路进行分析和实现，最后用Matlab对整个系统进行仿真，实验结果论证了该方法的可行性．这样使得混沌脉冲定位调制信号可以利用现有的混沌映射实现．从而具有多样性和稳定的混沌特性。也使得混沌脉冲定位调制（CPPM）技术具有更多的实现途径和更深的研究与应用价值。     

Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach

Sampled-data feedback control for master-slave synchronization schemes that consist of identical chaotic Lur'e systems is studied. Sufficient conditions for global asymptotic synchronization of such chaotic Lur'e systems are obtained using the free-weighting matrix approach and expressed in terms of linear matrix inequalities (LMIs). With the help of the LMI solvers, the sampled-data feedback control law can easily be obtained to globally asymptotically synchronize Lur'e chaotic systems. The effectiveness of the proposed method is finally illustrated via numerical simulations of chaotic Chua's circuits.     

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...     

基于单电子器件的蔡氏电路实现

基于提出的单电子晶体管和MOS混合器件构成的非线性电阻电路以及CMOS构建的模拟电感,实现了一种新型蔡氏混沌电路,得到其双涡卷混沌吸引子.研究表明,该混沌电路具有结构简单、功耗较低,实现效果好、集成度高等优点,为混沌电路在理论和实践方面提供了新的硬件基础,同时,也为保密通信领域提供了又一种可行的实现方法.     

Inductorless Chua's circuit

The famous chaotic oscillator known as Chua's circuit, despite the robustness of the chaotic behaviour to parametric mismatches, requires the construction of noncommercial valued inductors. A low cost inductorless version of Chua's circuit is presented. It is argued that the new circuit is better suited for control and synchronisation purposes     

SETMOS器件在混沌保密通信中的应用研究

采用拟合法对SETMOS器件的负微分电阻特性曲线进行研究,得到了它的简化模型,通过细胞神经网络（CNN）结构研究了由SETMOS实现变型蔡氏电路的途径,并分析了该电路的基本混沌动力学行为,如相图、分岔及功率谱等;进一步利用自适应反馈法实现了变型蔡氏电路的混沌同步设计,并将其应用到保密通信领域。理论分析和仿真结果验证了电路设计的正确性及有效性。研究结果表明,所设计的混沌同步电路结构简单,易于纳电子器件的大规模集成和应用。     

Design of a tensile-type 3-D multi-scroll chaotic system and its application in secure communication

A kind of tensile-type 3-D multi-scroll chaotic attractor based on Chua's circuit was successfully designed. The chaos generation mechanism was studied by analyzing the symmetry and invariance, the existence of the dissipation, as well as the system equilibrium and stability. Then, some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic dynamical behaviors of the new chaotic system were introduced, either numerically or analytically. At the same time, the chaotic circuit of this system was realized by PSPICE. Finally, based on Lyapunov theorem and unidi-rectionally coupled method, the synchronization of the chaotic system has also been investigated. With this approach, the novel system can be applied to secure communication, which can achieve the purpose of covering specific signals. The experimental results are in agreement with numerical simulation results, which verifies the availability and feasibility of this method.     

基于Chua电路混沌同步自保持特性的研究

本文介绍了Chua电路及其特性，给出实现非线性电阻的一种电路；利用Chua电路构造出一种驱动-响应混沌同步系统，利用仿真得出此同步系统具有一定鲁捧性，抗干扰等特性；根据此同步系统，仿真发现混沌同步具有自保持特性，并给出仿真结果，这一发现为混沌在保密通信的实际应用提供了依据．