分数阶Chua's系统错位同步无感模块化电路实现及应用

基于分数阶混沌系统稳定性理论, 设计高效的非线性控制器, 实现初始值不同的两个分数阶Chua's系统错位投影同步. 根据分数阶复频域近似方法, 提出分数阶系统的等效电路, 实现分数阶Chua's系统错位投影同步的无感模块化电路. 最后,利用改进的混沌掩盖通信原理, 将以上同步方案应用于混沌保密通信中, 在发送端使用分数阶混沌序列对有用信号加密传送, 从接收端可以无失真地恢复出有用信号. 数值仿真与电路仿真证实了提出方案的可行性. 关键词： 分数阶Chua's系统 错位投影同步 无感模块化电路 保密通信     

基于单驱动变量的混沌广义投影同步及在保密通信中的应用

基于单向耦合提出一种只需传递一个驱动变量实现混沌系统广义投影同步方法.通过改变广义投影同步的比例因子,获得任意比例于原驱动混沌系统输出的混沌信号.由于只需传递一个信号,比起已有的方法具有更高的实用价值,理论推导和数值仿真进一步表明了该方法的有效性.最后,基于统一混沌系统的广义投影同步,给出了一种安全性更好的混沌保密通信方案. 关键词： 混沌系统 单驱动变量 广义投影同步 统一混沌系统     

混沌系统的统一投影同步

提出一种实现混沌系统投影同步的统一方法.通过构建一个广义比例矩阵和一个合适的响应系统,建立了混沌投影同步的通用模型,依据比例矩阵的不同种类,可实现广义投影同步、错位投影同步和广义混合错位投影同步等各种类型的混沌投影同步.利用Lyapunov稳定性理论给出了相应的证明,最后以多卷波混沌系统和超混沌Qi系统为例,进行了错位投影同步和广义混合错位投影同步的数值仿真,仿真结果进一步表明了该方法的有效性. 关键词： 混沌系统 广义比例矩阵 统一投影同步     

SC混沌比例投影同步方法在保密通信中的应用

利用基于线性稳定性准则的SC混沌比例投影同步方法,提出一种应用于保密通信的混沌掩盖方案.适当分离出混沌系统的线性项与非线性项,构造一个非线性驱动向量函数,混沌状态变量包含用于投影同步的比例因子,把所需传递的有用信息掩盖入其中一个分量上,得到混沌载波信号,提高加密信息的复杂度和解码的困难度.以Lorenz吸引子和超混沌Rössler吸引子为例进行数值仿真,详细分析传输的正弦信息加密解密全过程,给出简单、最优的混沌掩盖方案,数值分析证明比例投影同步方法应用于保密通信领域的有效性.     

基于两级混沌同步保密通信方案的设计

设计了基于混沌双重加密的混沌同步保密通信方案,用以改善保密通信系统的安全性. 一级加密采用了具有2种反馈的同步混沌系统,二级加密采用了超混沌系统. 仿真结果成功地还原了原文信号,证明所设计系统能够更有效的避免现有的基于混沌保密通信破译方法的攻击.     

复杂Dynamos混沌系统的追踪控制与同步

基于系统稳定性理论，设计合适的新型非线性反馈控制器，实现复杂Dynamos混沌系统的状态向量与任意给定的不同参考信号追踪广义投影同步.以追踪控制超混沌系统、混沌系统、正弦余弦信号以及不动点为例，通过改变比例因子，可以获得多个不同混沌系统之间的异结构广义投影同步以及与正弦波形的广义同步，或者将复杂Dynamos混沌系统控制到期望的平衡点.数值仿真进一步表明了该方法的有效性.     

复杂Dynamos混沌系统的追踪控制与同步

基于系统稳定性理论,设计合适的新型非线性反馈控制器,实现复杂Dynamos混沌系统的状态向量与任意给定的不同参考信号追踪广义投影同步.以追踪控制超混沌系统、混沌系统、正弦余弦信号以及不动点为例,通过改变比例因子,可以获得多个不同混沌系统之间的异结构广义投影同步以及与正弦波形的广义同步,或者将复杂Dynamos混沌系统控制到期望的平衡点.数值仿真进一步表明了该方法的有效性. 关键词： 复杂Dynamos混沌系统 追踪控制 广义投影同步 平衡点     

参数不确定时延超混沌系统的脉冲同步方法研究

针对一类参数不确定的异构时延超混沌系统,采用响应系统与驱动系统状态变量误差的线性反馈作为脉冲控制信号,基于Lyapunov稳定性理论实现了超混沌系统的脉冲同步,给出了渐近稳定条件,并构造了一个具有时延的数字保密通信系统.该方案保密性高,鲁棒性强.数值仿真表明系统能快速达到同步,应用混沌密码序列对数字信号进行加密后,信息信号可以在接收端有效地恢复出来. 关键词： 时延 脉冲同步 数字保密通信     

基于线性分离的自治混沌系统的投影同步

分析了自治混沌系统的投影同步问题.基于线性系统的稳定判定准则，提出一种新的线性分离的同步方法，并采用该方法实现了Lorenz系统，Rssler系统和超混沌Chen系统的投影同步.数值模拟进一步验证了所提出方案的有效性. 关键词： 投影同步 自治混沌系统 线性分离     

参数不确定的分数阶混沌系统广义错位延时投影同步

为进一步增强通信系统中保密通信的安全性,结合广义错位投影同步和延时投影同步,提出了广义错位延时投影同步.以分数阶Chen系统和Lü系统为例,针对两系统参数都不确定,基于分数阶稳定性理论与自适应控制方法,设计了非线性控制器和参数自适应律,实现了广义错位延时同步,并辨识出驱动系统和响应系统中所有不确定参数.理论分析和数值仿真验证了该方法的可行性与有效性.     

Hybrid projective synchronization of chaotic fractional order systems with different dimensions

The hybrid projective synchronization of different dimensional fractional order chaotic systems is investigated in this paper. It is shown that the slave system can be synchronized with the projection of the master system generated through state transformation. Based on the stability theorem of linear fractional order systems, a suitable controller for achieving the synchronization is given. The hybrid projective synchronization between the fractional order chaotic system and hyperchaotic system is successfully achieved in both reduced order and increased order. The corresponding numerical results verify the effectiveness of the proposed method.     

Lag projective synchronization in fractional-order chaotic (hyperchaotic) systems

In this Letter, a new lag projective synchronization for fractional-order chaotic (hyperchaotic) systems is proposed, which includes complete synchronization, anti-synchronization, lag synchronization, generalized projective synchronization. It is shown that the slave system synchronizes the past state of the driver up to a scaling factor. A suitable controller for achieving the lag projective synchronization is designed based on the stability theory of linear fractional-order systems and the pole placement technique. Two examples are given to illustrate effectiveness of the scheme, in which the lag projective synchronizations between fractional-order chaotic Rössler system and fractional-order chaotic Lü system, between fractional-order hyperchaotic Lorenz system and fractional-order hyperchaotic Chen system, respectively, are successfully achieved. Corresponding numerical simulations are also given to verify the analytical results.     

Adaptive modified function projective synchronization of multiple time-delayed chaotic Rossler system

In this Letter we consider modified function projective synchronization of unidirectionally coupled multiple time-delayed Rossler chaotic systems using adaptive controls. Recently, delay differential equations have attracted much attention in the field of nonlinear dynamics. The high complexity of the multiple time-delayed systems can provide a new architecture for enhancing message security in chaos based encryption systems. Adaptive control can be used for synchronization when the parameters of the system are unknown. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems are function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

Continuous-time chaotic systems： Arbitrary full-state hybrid projective synchronization via a scalar signal

Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic （hyperchaotic） systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.     

改进恒Lyapunov指数谱混沌系统的广义投影同步研究

对改进恒Lyapunov指数谱混沌系统的广义投影同步进行了研究.用主动控制同步法设计合适的非线性反馈控制器,通过单向耦合,实现恒指数谱混沌系统的同结构广义投影同步与异结构广义投影同步.在指出广义投影同步体系中比例因子调节作用的同时,也分析了改进恒指数谱混沌系统的全局线性调幅参数对同步体系中两个系统的作用.基于模块与复用的设计思想,详细分析并构建了广义投影同步体系中的驱动系统、控制系统与响应系统.数值仿真与电路实验仿真一致显示：调节比例因子能够获得任意比例于原驱动混沌系统输出的混沌信号;调节全局线性调幅参数,能够同时线性调整同步体系中两个系统输出的状态变量的幅值,而不影响两个系统之间的广义投影同步. 关键词： 改进恒Lyapunov指数谱混沌系统 广义投影同步 比例因子 全局线性调幅参数     

A function cascade synchronization method with unknown parameters and applications

This paper investigates the function cascade synchronization of chaos system. Combining cascade synchronization scheme, parametric adaptive control and projective synchronization scheme, it proposes a new function cascade synchronization scheme to address a generalized-type synchronization problem of three famous chaotic systems： the Lorenz system, Liu system and RSssler system, the states of two identical chaotic systems with unknown parameters can be asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.     

A function cascade synchronization method with unknown parameters and applications

This paper investigates the function cascade synchronization of chaos system. Combining cascade synchronization scheme, parametric adaptive control and projective synchronization scheme, it proposes a new function cascade synchronization scheme to address a generalized-type synchronization problem of three famous chaotic systems: the Lorenz system, Liu system and R\"{o}ssler system, the states of two identical chaotic systems with unknown parameters can be asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.     

Function projective synchronization of two-cell quantum-CNN chaotic oscillators by nonlinear adaptive controller

In this Letter, we investigate function projective synchronization of two-cell quantum-CNN chaotic oscillators using nonlinear adaptive controller. Based on Lyapunov stability theory, the nonlinear adaptive control law is derived to make the state of two chaotic systems function projective synchronized. Two numerical simulations are presented to illustrate the effectiveness of the proposed nonlinear adaptive control scheme, which is more effective than that in previous literature.     

Modified scaling function projective synchronization of chaotic systems

This paper investigates a kind of modified scaling function projective synchronization of uncertain chaotic systems using an adaptive controller. The given scaling function in the new method can be an equilibrium point, a periodic orbit, or even a chaotic attractor in the phase space. Based on LaSalle's invariance set principle, the adaptive control law is derived to make the states of two chaotic systems function projective synchronized. Some numerical examples are also given to show the effectiveness of the proposed method.