Multiparameter estimation using only a chaotic time series and its applications

An important extension to the techniques of synchronization-based parameter estimation is presented. Based on adaptive chaos synchronization, several methods are proposed to dynamically estimate multiple parameters using only a scalar chaotic time series. In comparison with previous schemes, the presented methods decrease the cost of parameter estimation and are more applicable in practice. Numerical examples are used to demonstrate the effectiveness and robustness of the presented methods. As an example application, an implementation of multichannel digital communication is proposed, where multiparameter modulation is used to simultaneously transmit more than one digital message. From a theoretical perspective, such an encoding increases the difficulty to directly read out the message from the transmitted signal and decreases the implementation cost.     

A new chaotic communication scheme based on adaptive synchronization

A new chaotic communication scheme using adaptive synchronization technique of two unified chaotic systems is proposed. Different from the existing secure communication methods, the transmitted signal is modulated into the parameter of chaotic systems. The adaptive synchronization technique is used to synchronize two identical chaotic systems embedded in the transmitter and the receiver. It is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical unified chaotic systems with unknown system parameters asymptotically synchronized; thus the parameter of the receiver system is identified. Then the recovery of the original information signal in the receiver is successfully achieved on the basis of the estimated parameter. It is noticed that the time required for recovering the information signal and the accuracy of the recovered signal very sensitively depends on the frequency of the information signal. Numerical results have verified the effectiveness of the proposed scheme.     

Decoding information by following parameter modulation with parameter adaptive control

It has been proposed to realize secure communication using chaotic synchronization via transmission of a binary message encoded by parameter modulation in the chaotic system. This paper considers the use of parameter adaptive control techniques to extract the message, based on the assumptions that we know the equation form of the chaotic system in the transmitter but do not have access to the precise values of the parameters which are kept secret as a secure set. In the case in which a synchronizing system can be constructed using parameter adaptive control by the transmitted signal and the synchronization is robust to parameter mismatches, the parameter modulation can be revealed and the message decoded without resorting to exact parameter values in the secure set. A practical local Lyapunov function method for designing parameter adaptive control rules based on originally synchronized systems is presented.     

量子阱激光器混沌相位控制同步以及编码研究

提出外部光注入多量子阱激光器激光混沌相位控制同步，及其混沌相位相移键控外调制ON/ON全光保密通信系统，数值模拟了在相位控制器控制下的激光混沌同步.通过连续ON/ON键控调制相位控制器调制通过相位控制器的激光相位相移，实现激光混沌相位相移键控连续调制，设置接收系统相位控制器，控制通过接收相位控制器的激光相位相移，以实现激光混沌解调.分别数值模拟了该系统调制速率01和05Gbit/s混沌相位相移ON/ON键控通信，进行了混沌ON/ON键控调制速率分析，以及系统参数失配和系统抗噪声扰动的数值分析. 关键词： 混沌 同步 通信 多量子阱激光器     

光纤混沌相位编码保密通信系统理论研究

通过耦合激光混沌相位控制同步系统和光纤信道，提出外部光注入半导体激光器激光混沌相 位控制光纤同步以及混沌相位相移键控外调制光纤保密通信系统理论模型，数值实现了在相 位控制器控制下的远程光纤混沌同步.理论分析了光纤自相位调制对混沌信号以及对同步的 影响，导出了光纤混沌最大传输距离公式.通过连续键控调制相位控制器实现了光纤激光混 沌相位相移键控编码调制发射，设置接收系统相位控制器控制激光相位相移实现了光纤激光 混沌同步解调.数值模拟了具有比特率50Mbit/s远程光纤混沌数字编码通信系统的应用，详 细地进行了在远距离光纤传输中的系统参数失配以及系统抗噪声能力的数值分析. 关键词： 混沌 同步 光纤混沌通信 半导体激光器 相位     

时空混沌系统参量辨识律的设计与投影同步研究

研究了相互耦合的时空混沌系统的参量辨识与投影同步问题. 依据Lyapunov定理, 设计了参量辨识律和表征耦合强度的待定函数的自适应律, 对响应系统中的未知参量进行了有效辨识, 并完成了时空混沌系统的投影同步研究. 采用具有时空混沌行为的Burgers方程作为实例进行了仿真分析.     

Adaptive synchronization of a switching system and its applications to secure communications

This paper studies the adaptive synchronization of a switching system with unknown parameters which switches between the R?ssler system and a unified chaotic system. Using the Lyapunov stability theory and adaptive control method, the receiver system will achieve synchronization with the drive system and the unknown parameters would be estimated by the receiver. Then the proposed switching system is used for secure communications based on the communication schemes including chaotic masking, chaotic modulation, and chaotic shift key strategies. Since the system switches between two chaotic systems and the parameters are almost unknown, it is more difficult for the intruder to extract the useful message from the transmission channel. In addition, two new schemes in which the chaotic signal used to mask (or modulate) the transmitted signal switches between two components of a chaotic system are also presented. Finally, some simulation results are given to show the effectiveness of the proposed communication schemes.     

A discrete-time chaos synchronization system for electronic locking devices

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.     

New communication schemes based on adaptive synchronization

In this paper, adaptive synchronization with unknown parameters is discussed for a unified chaotic system by using the Lyapunov method and the adaptive control approach. Some communication schemes, including chaotic masking, chaotic modulation, and chaotic shift key strategies, are then proposed based on the modified adaptive method. The transmitted signal is masked by chaotic signal or modulated into the system, which effectively blurs the constructed return map and can resist this return map attack. The driving system with unknown parameters and functions is almost completely unknown to the attackers, so it is more secure to apply this method into the communication. Finally, some simulation examples based on the proposed communication schemes and some cryptanalysis works are also given to verify the theoretical analysis in this paper.     

复Ginzburg-Landau方程时空混沌的网络同步与参量辨识

研究了参量未知的时空混沌系统构成复杂网络的同步与参量辨识问题. 设计的参量辨识律可以有效地辨识复杂网络中所有节点时空混沌系统中的未知参量. 基于稳定性定理, 通过构造适当的Lyapunov函数, 确定了网络完全同步的条件. 以参量未知的一维复Ginzburg-Landau方程作为网络节点为例, 通过仿真模拟检验了参量辨识律以及同步方法的有效性.     

适合传输快变信息信号的混沌调制保密通信

提出一种新的混沌调制通信方法.利用一个自适应控制器跟踪信息信号的误差对产生混沌载波的发射系统进行参数调制.同时，信息信号直接与混沌载波相乘作为发射信号驱动接收系统.在接收端，另一个自适应控制器维持收发系统的混沌同步并恢复出信息信号.由于同步误差与信息信号无关，从而实现了大幅度、快时变信息信号的混沌调制通信.理论分析和数值模拟的结果表明该方法增强了低维混沌系统的通信保密性. 关键词： 混沌调制 保密通信 自适应控制器 蔡氏电路     

利用混沌信号幅值实现混沌同步

构造了一个三维混沌系统, 简要分析了该混沌系统的平衡点性质、混沌吸引子相图和Lyapunov指数等特性. 在此基础上, 利用反馈同步思想设计了一种利用混沌信号部分信息实现混沌同步的方法, 完成了三维混沌系统的同步. 该方法仅利用混沌信号幅值信息即可实现两个混沌系统的同步, 其同步建立与混沌信号的极性无关, 此特性可有效提高混沌通信质量. 通过分析系统的条件Lyapunov指数证实该方法的有效性, 数值仿真表明该方法与利用混沌信号全部信息的线性反馈同步法相比, 同步建立时间基本相同.     

Using polarization properties to enhance performance of chaos synchronization communication between vertical-cavity surface-emitting lasers

Enhanced chaos synchronization communication between vertical-cavity surface-emitting lasers (VCSELs) is investigated numerically, by adopting a polarization communication protocol where one polarization mode is used as the chaotic carrier and the orthogonal polarization mode is used as the disturbed signal. The chaos synchronization quality for the receiver laser (RL) and attacker laser (AL) are analyzed in terms of the cross-correlation coefficient. There are two distinct regions of good synchronization quality in the injection parameters space. In the first region, good synchronization quality can be ensured for both the RL and AL. In the second region, only the RL can realize chaos synchronization. We further discuss the security enhancement by comparing the communication performance between RL and AL for injection parameters within the second region. The results show that successful and robust decoding is only achievable for the RL.     

Parameter identification and synchronization of spatiotemporal chaos in an uncertain Gray-Scott system

The zero-asymptotic property of sliding variables in discrete systems is extended to a continuous one and applied to partial differential equations which describe spatiotemporal chaos. A method of chaos synchronization and parameter identification is proposed. The synchronization controllers and the parameter recognizers are designed. The uncertain Gray-Scott system is taken as an example to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizers may take the place of the unknown parameters in both target and response systems. Global synchronization of the two spatiotemporal chaotic systems with uncertain parameters may be realized quickly after controllers are added. Supported by the Natural Science Foundation of Liaoning Province, China (Grant No. 20052151) and the Innovative Team Program of Liaoning Educational Committee     

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.     

Generalized synchronization of chaos in identical systems with hidden degrees of freedom

We demonstrate generalized synchronization of chaos in a two-mode laser system. The total intensity of the laser output (the sum of the individual mode intensities) is used as the drive signal. This lumped variable transmitted to the identical response system does not generate identical synchronization. Generalized synchronization is observed instead of identical synchronization because of the hidden internal degrees of freedom.     

偏振态移位键控光混沌通信系统的保密性

为了评判偏振态移位键控(PolSK)光混沌通信系统的保密性强弱,先要验证它的混沌特性,因此对该系统的信号进行了分析。利用三种方法判定该信号是否具有混沌特性:在三维相空间观察奇异吸引子;分别从最大李氏(Lyapunov)指数满足的方程出发以及wolf法计算其最大李氏指数;并计算其自功率谱密度函数。结果明显观察到奇异吸引子,算得最大李氏指数分别为0.0364和0.0106,都大于零,自功率谱为噪声背景、宽峰的连续谱;从而判定该系统传输的信号确实是混沌信号。另一方面,用最小伪邻点算法计算该系统信号的嵌入维数,结果达到6维,说明该系统具有中高维度混沌特性;结合系统的抗攻击性分析,得出结论:相比于一般的混沌掩盖方案,该系统具有较强的保密性和安全性。     

一阶时滞混沌的参数辨识

估计混沌系统的未知参数是混沌控制与同步中必须解决的关键问题.针对两种不同类型的时滞混沌系统中的未知参数的辨识问题，将系统的未知参数看作系统的未知状态，利用非线性状态观测器理论进行参数估计，通过选取观测器中非线性增益函数，使得闭环误差系统指数或渐进稳定，从而给出参数估计器存在的充分条件.以典型的时滞Logistic系统为例进行了数值模拟，数值仿真结果表明，使用该方法可以对时滞混沌系统的未知参数进行有效地估计.     

Bidirectional chaos synchronization and communication based on mutually coupled semiconductor lasers with asymmetrical bias currents

In this paper, a bidirectional chaos secret communication system, based on mutually coupled semiconductor lasers (MCSLs) with asymmetrical bias currents, is proposed, and the synchronization characteristics and the communication performances of such a system are numerically investigated. The results show that the stable leader-laggard chaos synchronization can be achieved under relatively large asymmetrical bias current levels. Meantime, the influence of the intrinsic parameter variations of the laser on the synchronization quality is also considered, and the simulation reveals that this system still possesses good robustness to the parameter variations. Moreover, the influences of delay time and mutually coupling strength between the two lasers on chaos communication performance have also been discussed. Finally, unidirectional and bidirectional secret communication performances of such a system are examined under the chaos masking (CMS) encryption scheme, and the security of this system is also discussed.     

Communicating with noise: How chaos and noise combine to generate secure encryption keys

An approach for the secure transmission of encrypted messages using chaos and noise is presented in this paper. The method is based on the synchronization of certain types of chaotic oscillators in response to a common noise input. This allows two distant oscillators to generate identical output which can be used as a key for encryption and decryption of a message signal. The noiselike synchronizing input-which contains no message information-is communicated to identical oscillators in the transmitter and the receiver over a public channel. The encrypted message is also sent over a public channel, while the key is never transmitted at all. The chaotic nature of the oscillators which generate the key and the randomness of the signal driving the process combine to make the recovery of the key by an eavesdropper extremely difficult. We evaluate system performance with respect to security and robustness and show that a robust and secure system can be obtained. (c) 1998 American Institute of Physics.