一类参数未知超混沌系统的广义函数投影滞后同步

混沌系统同步问题的研究是混沌保密通信技术研究的重要理论基础。针对函数投影同步中对时滞现象研究较少的问题,基于Lyapunov稳定性定理和自适应控制方法,设计了相应的自适应控制器和参数更新规则,实现了一类超混沌系统之间的广义函数投影滞后同步,以超混沌LS系统和超混沌Lü系统为例,验证理论的正确性和有效性,同时分析了外加噪声干扰和延时对同步控制效果的影响。数值仿真结果证实了所提方法的有效性、可行性和鲁棒性。     

一个新的四维超混沌系统的滞后同步及其Simulink仿真

针对一个新的四维超混沌系统,研究了它的滞后同步和参数辨识问题。基于Lyapunov稳定性定理和自适应控制方法,利用误差系统的状态反馈量设计控制器,在通道有无噪声的两种情况下,实现了该系统的滞后同步,同时辨识出所有未知参数,控制器的控制强度也可以自适应确定。最后采用Simulink数值仿真验证了理论的正确性、有效性和鲁棒性。     

基于改进的超混沌系统修正射影同步算法研究

研究超混沌修正射影同步算法问题。由于修正射影同步不可预测的伸缩矩阵因子能够有效地提高保密通信的安全性,所以它在保密通信中有着非常诱人的应用前景,但是传统的同步射影算法由于较高的计算复杂度,难以得到广泛应用。针对上述问题,提出了一种新的基于超混沌系统修正射影同步算法。该方法首先给出了一个比已知的射影同步更一般形式的新同步,之后采用激活控制方法使两个一致的超混沌系统整体同步。最后算法在基于软件Maple和稳定性理论基础上,通过数值仿真同步的结果表明,提出的算法能够自主选择调节缩放矩阵中的比例因子,可以较好地满足状态控制器设计的射影同步,降低了算法的复杂性。     

超混沌吕系统的滞后投影同步与参数识别

研究了超混沌吕系统的滞后投影同步与系统参数识别.在响应系统中加入适当的非线性控制器,利用Lyapunov稳定性方法和Barbalat引理进行理论分析证明,实现了驱动响应系统之间所有变量的全局滞后投影同步,并能够对超吕系统的未知参数进行识别.最后通过数值仿真对本文中提出的理论方法的正确性及可行性进行验证.     

超混沌Rossler系统和超混沌Lorenz系统的全状态混合投影同步

用两种不同的方法一主动控制法和自适应控制法实现超混沌Rossler系统和超混沌Lorenz系统的异结构全状态混合投影同步,各自设计了不同的控制器,使得响应系统与驱动系统同步．当参数已知时,采用主动控制法,方法简单有效且不需要构造Lyapunov函数,实现同步的时间短;当系统参数部分未知或完全未知时,基于Lyapunov稳定性理论,给出自适应同步控制器的系统性设计过程和参数自适应律,使得系统间迅速达到同步．数值模拟验证了两种方法的有效性．     

Synchronization and control of hyperchaotic complex Lorenz system

The aim of this paper is to investigate the phenomenon of projective synchronization (PS) and modified projective synchronization (MPS) of hyperchaotic attractors of hyperchaotic complex Lorenz system which has been introduced recently in our work. The control problem of these attractors is also studied. Our system is a 6-dimensional continuous real autonomous hyperchaotic system. The active control method based on Lyapunov function is used to study PS and MPS of this system. The problem of hyperchaos control is treated by adding the complex periodic forcing. The control performances are verified by calculating Lyapunov exponents. Numerical simulations are implemented to verify the results of these investigations.     

Synchronization and control of hyperchaotic complex Lorenz system

The aim of this paper is to investigate the phenomenon of projective synchronization (PS) and modified projective synchronization (MPS) of hyperchaotic attractors of hyperchaotic complex Lorenz system which has been introduced recently in our work. The control problem of these attractors is also studied. Our system is a 6-dimensional continuous real autonomous hyperchaotic system. The active control method based on Lyapunov function is used to study PS and MPS of this system. The problem of hyperchaos control is treated by adding the complex periodic forcing. The control performances are verified by calculating Lyapunov exponents. Numerical simulations are implemented to verify the results of these investigations.     

新超混沌系统的动力学行为及自适应控制和同步

分析了一个新混沌系统的超混沌动力学行为,给出了这个未知参数的超混沌系统的自适应控制和同步问题的数值模拟结果.运用相图、分岔图、Lyapunov指数谱和庞加莱截面图,返回映射和功率谱等揭示了系统混沌行为的普适特征,基于Lyapunov稳定性理论,采用自适应控制方法将系统的混沌运动控制到一个不稳定的平衡点.此外,设计自适应控制律以实现超混沌系统的状态同步,仿真结果表明所提出的方法的有效性.     

基于反步法的混沌系统函数投影同步

针对最新提出的Lü混沌系统和超Lü混沌系统的耦合系统,在响应系统中加入控制项v,通过变换和反步设计,利用Lyapunov稳定性理论,实现了驱动-响应耦合系统之间的函数投影同步,使驱动响应系统之间按照任意给定的有界尺度函数α(t)演化.数值试验验证了理论分析的正确性.     

自适应超混沌系统修正广义同步及其电路实现

运用自适应控制方法,实现超混沌Chen系统的同结构投影同步,并能辨识出响应系统的未知参数。首先通过采用MATLAB进行数字仿真,表明该自适应控制方法的可行性以及系统的参数辨识作用。其次利用EWB仿真设计模拟电路,结果与MATLAB的仿真结果相吻合,从而进一步证明了该自适应控制方法的有效性和系统参数辨识方法。     

Weak projective lag synchronization of neural networks with parameter mismatch

This paper studies projective lag synchronization of coupled neural networks with time delay and parameter mismatch. An adaptive controller is designed to achieve weak projective lag synchronization of coupled neural networks. This method is employed to realize projective lag synchronization between coupled neural systems with an error level. Numerical simulation illustrates the effectiveness of the results.     

Projective synchronization of two different fractional-order chaotic systems via adaptive fuzzy control

In this paper, the projective synchronization problem of two fractional-order different chaotic (or hyperchaotic) systems with both uncertain dynamics and external disturbances is considered. More particularly, a fuzzy adaptive control system is investigated for achieving an appropriate projective synchronization of unknown fractional-order chaotic systems. The adaptive fuzzy logic systems are used to approximate some uncertain nonlinear functions appearing in the system model. These latter are augmented by a robust control term to compensate for the unavoidable fuzzy approximation errors and external disturbances as well as residual error due to the use of the so-called e-modification in the adaptive laws. A Lyapunov approach is adopted for the design of the parameter adaptation laws and the proof of the corresponding stability as well as the asymptotic convergence of the underlying synchronization errors towards zero. The effectiveness of the proposed synchronization system is illustrated through numerical experiment results.     

不确定参数下的四维超混沌吕系统的最优同步

研究了最新提出的超混沌吕系统的最优同步问题.利用哈密顿-雅可比-贝尔曼方程,对具有不确定参数的超混沌吕系统设计了最优同步的方案,分别得到了无限时间区间和有限时间区间上的最优控制器和参数控制律.数值仿真验证了理论分析的正确性.     

异构超混沌广义同步系统构造及其电路仿真

在三维新混沌Chen系统基础上构建了一个四维超混沌系统。根据Lyapunov稳定性原理,采用自适应控制方法,在新构建的四维超混沌系统和四维超混沌Chen系统之间设计广义同步控制器,对控制器中的变量参数估计值和外部参数值进行广义同步实现的可行性进行讨论,进而将异构系统的广义同步问题转换为对控制器的选择。通过对不同参数估计值的比较分析得出合适的取值,达到了良好的广义同步效果。最后设计了一种实现广义混沌同步的基本电路原理图,数值仿真和电路实验结果表明了该方法的有效性,以及电路的可行性和实用性。     

Global projective lag synchronization of fractional order memristor based BAM neural networks with mixed time varying delays

This paper addresses Master–Slave synchronization for some memristor‐based fractional‐order BAM neural networks (MFBNNs) with mixed time varying delays and switching jumps mismatch. Firstly, considering the inherent characteristic of FMNNs, a new type of fractional‐order differential inequality is proposed. Secondly, an adaptive switching control scheme is designed to realize the global projective lag synchronization goal of MFBNNs in the sense of Riemann‐Liouville derivative. Then, based on a suitable Lyapunov method, under the framework of set‐valued map, differential inclusions theory, fractional Barbalat's lemma and proposed control scheme, some new projective lag synchronization criteria for such MFBNNs are obtained. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed theoretical analysis.     

一个新的超混沌系统及其线性反馈同步*

绝对值项的非线性化作用往往可以代替平方项,Liu等人提出的类Lorenz系统中平方项用绝对值代替,并利用合适的反馈控制手段,可以构造一种新的含有绝对值项的超混沌系统。利用相图、Lyapunov指数、庞加莱映射与频谱分析等手段,证明了该系统是超混沌系统。利用线性反馈同步控制理论实现了新构造的超混沌系统的同步。数值仿真证明,只要选择合适的线性反馈控制增益矢量,就可以容易地实现驱动系统与响应系统之间的快速同步。     

带有不确定性的不同超混沌系统的同步及其在保密通信中的应用

基于Lyapunov稳定性理论,给出了带有不确定参数和外界扰动的超混沌Lu系统与超混沌R／Sssler系统同步的自适应控制器及参数更新律．系统一旦达到同步,隐藏在发射系统中的信息信号能够在接收系统中得到准确恢复．这里的同步策略只需要利用未知参数和外界扰动的有界性,不需要求出其具体的边界及Lipschitz常数值．数值模拟验证了该方案的有效性．     

自适应线性广义同步方法

针对参数未知混沌系统提出一种自适应线性广义同步方案,并用该方案实现参数未知统一超混沌系统的自适应线性广义同步,同时用该控制方案对参数未知统一超混沌系统进行参数识别。     

超混沌Lü系统的线性与非线性耦合同步

针对由Aiminchen等人最近提出来的一个新的超混沌系统—超混沌Lü系统的同步问题展开研究.对两个恒同的超混沌Lü系统,分别给出了它们在线性耦合和非线性耦合情形下在全局范围内实现同步的充分条件,用Lyapunov方法从理论上证明了结论,并用数值仿真验证了理论结果.     

Some new criteria for lag synchronization of chaotic Lur＇e systems by replacing variables control

Some new criteria for the chaotic lag synchromzation are proposed. At first, lag synchronization scheme for identical master-slave Lur‘e systems by replacing variables control and the relevant error system are given, and the relations between absolute stability of the error system and the chaotic lag synchromzation are described. Then. based on a quadratic Lyapunov function, two new Lur‘e criteria for the above chaotic lag synchronization are proved. Four corresponding frequency domain criteria are further derived by means of Meyer-Kalman-Yacubovia Lemma. These frequency domain criteria are apphed to analyze the lag synchromzation of general master-slave Chua‘s circuits so that some ranges of the parameters in which the master-slave Chua‘s circuits achieve chaotic lag synchronization by replacing single-variable control are attained. Finally, some examples are given to verify the theoretical results.