Bidirectional Partial Generalized Synchronization in Chaotic and Hyperchaotic Systems via a New Scheme

In this paper, a bidirectional partial generalized (lag, complete, and anticipated) synchronization of a class of continuous-time systems is defined. Then based on the active control idea, a new systematic and concrete scheme is developed to achieve bidirectional partial generalized (lag, complete, and anticipated) synchronization between two chaotic systems or between chaotic and hyperchaotic systems. With the help of symbolic-numerical computation, we choose the modified Chua system, Lorenz system, and the hyperchaotic Tamasevicius-Namajunas-Cenys system to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. It is interesting that partial chaos synchronization not only can take place between two chaotic systems, but also can take place between chaotic and hyperchaotic systems. The proposed scheme can also be extended to research bidirectional partial generalized (lag, complete, and anticipated) synchronization between other dynamical systems.     

Chaotic cryptology

A method to transfer secret information using chaotic dynamical systems is proposed. It is based on modulating a chaotic system with the message such that its time evolution contains the hidden information. Decryption of the cipher is achieved by chaos control. Operation of the scheme is demonstrated by en- and decoding a short german text.     

Impulsive Control for Fractional-Order Chaotic Systems

We propose an impulsive control scheme for fractional-order chaotic systems. Based on the Takagi-Sugeno （T-S） fuzzy model and linear matrix inequalities （LMfs）, some sufficient conditions are given to stabilize the fractional-order chaotic system via impulsive control. Numerical simulation shows the effectiveness of this approach.     

Fuzzy Modeling and Impulsive Control of a Memristor-Based Chaotic System

We mainly investigate the issues of fuzzy modeling and impulsive control of a memristor-based chaotic system and present a memristor-based chaotic system as the Takagi-Sugeno model-based fuzzy system. Then, based on the impulsive control theory of dynamical systems, a criterion ensuring impulsive stabilization of the memristorbased chaotic system is derived for the first time. An illustrative example is given to verify the effectiveness of the control scheme.     

基于改善关联性Buck变换器的混沌控制

由于Buck变换器具有非线性特性, 在一定参数条件下, 它会处于混沌状态, 此时Buck变换器不能正常工作. 为了抑制Buck变换器的混沌现象, 本文首先建立了Buck变换器的精确状态方程模型, 然后通过分析可控范围图、开关逻辑图、相图、电感电流波形、输出电压波形, 研究了基于改善Buck变换器的电感电流与输出电压之间关联性的混沌控制策略. 研究结果表明: 该控制策略能够将处于混沌状态的Buck变换器稳定在周期1, 2, 4, 8轨道, 且该控制策略不需要预先确定期望的目标轨道, 不依赖于Buck变换器的电路参数, 只取决于一个外部参数即耦合强度, 所以该控制策略同样适用于其他 拓扑结构的功率变换器. 关键词： 混沌控制 Buck变换器 关联性 耦合强度     

Adaptive Function Projective Synchronization of Discrete-Time Chaotic Systems

By backstepping control law and the active control method, adaptive function projective synchronization of 2D and 3D discrete-time chaotic systems with Uncertain parameters are investigated. To illustrate the effectiveness of the new scheme, some numerical examples are given.     

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discretetime chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.     

一种新的被控混沌系统抗干扰控制器设计方法

针对一类动态混沌系统,在干扰幅值增大而影响被控混沌系统镇定的情况下,提出了一种利用补偿控制系统(敏感系统)抑制干扰幅值影响的控制设计方法. 这种方法首先将该敏感系统与原被控混沌闭环系统互联,然后通过设计敏感系统的自适应状态反馈控制器,以保证被控混沌闭环系统在干扰幅值增加的情况下仍能够渐近保持原有的稳定性.最后,通过仿真实例进一步验证了本文结论的有效性.     

光电反馈混沌系统脉冲同步特性研究

提出光电反馈混沌状态下的混沌脉冲同步.首先, 对激光器的混沌动力学方程进行了数值分析, 通过改变反馈系数和脉冲系数来观测混沌状态的变化, 实现了对混沌激光器的控制;然后, 对脉冲同步方程进行数值分析, 给出了同步的模拟图.实验结果表明此方法能实现混沌同步.     

基于模糊滑模的有限时间混沌同步实现

提出了混沌同步有限时间实现问题.应用全程滑模控制技术，选择指数型终端滑模趋近律来设计滑模控制器，以实现一类混沌系统的状态同步.该设计方案针对混沌系统的参数不确定性和外界扰动，引入模糊基函数网络，在线估计不确定性和外部扰动的界值.同时该方案消除了滑模控制的到达阶段，状态始终保持在滑模面上，并能在有限时间内趋近于原点.最后以Duffing系统为例研究验证同步策略的可行性和有效性.     

A Novel Adaptive Observer-Based Control Scheme for Synchronization and Suppression of a Class of Uncertain Chaotic Systems

A novel adaptive observer-based control scheme is presented for synchronization and suppression of a class of uncertain chaotic system. First, an adaptive observer based on an orthogonal neural network is designed. Subsequently, the sliding mode controllers via the proposed adaptive observer are proposed for synchronization and suppression of the uncertain chaotic systems. Theoretical analysis and numerical simulation show the effectiveness of the proposed scheme.     

基于追踪控制的混沌异结构同步

针对连续混沌系统，提出一种混沌异结构同步追踪控制方案.利用Lyapunov方法证明了当受控系统满足Lipchitz条件时，即可使其状态输出指数收敛到任意给定的参考信号.设计的控制器结构对不同的混沌系统具有统一的形式，可实现任意混沌系统之间的异结构同步.数值仿真进一步表明了该方法的有效性. 关键词： 混沌系统 追踪控制 同步     

一类离散非线性混沌系统的观测器

研究了一类离散非线性混沌系统的观测器设计问题,得到利用系统的一个状态变量及其时间延迟变量可以实现混沌观测器和混沌系统的混沌同步.将此方法应用到两个混沌系统,结果表明本方法对一类混沌系统是有效的.     

Synchronization of Chaotic Optical Systems by Remote Feedback Controlling

A dynamical variable feedback scheme is proposed to synchronize chaotic motion of two identical and nearly identical laser systems with an injected signal. The feedback synchronization method works well while the conventional variable-replacement synchronization methods are not realizable. Various practical situations for synchronizing two chaotic laser systems located distance away from each other are taken into account. The application of this synchronization approach to wide range of practical systems is emphasized.     

一种基于遍历性的混沌加密新算法

分析了E.Álvarez密码系统的加密方法及其弱点,在此基础上给出了一种基于遍历性的混沌加密新算法。即以混沌系统的控制参数和初始点为密钥,迭代混沌映射以便产生一个比特链,在该比特链中搜索明文分组,记下迭代次数作为密文分组。新算法避免了E.Álvarez密码方案中的若干弱点,增强了密码系统的安全性。最后通过对Logistic映射的仿真研究,验证了新密码系统满足密码学中的混淆和散布特性,并进而阐明了新密码系统的有效性。     

Chaotic digital communication by encoding initial conditions

We investigate the possibility to improve the noise performance of a chaotic digital communication scheme by utilizing further dynamical information. We show that by encoding the initial information of the chaotic carrier according to the transmitting bits, extra redundance can be introduced into the segments of chaotic signals corresponding to the consecutive bits. Such redundant information can be exploited effectively at the receiver end to improve the noise performance of the system. Compared to other methods (e.g., differential chaos shift keying), straightforward application of the proposed modulation/demodulation scheme already provides significant performance gain in the low signal-to-noise ratio (SNR) region. Furthermore, maximum likelihood precleaning procedure based on the Viterbi algorithm can be applied before the demodulation step to overcome the performance degradation in the high SNR region. The study indicates that it is possible to improve the noise performance of the chaotic digital communication scheme if further dynamics information is added to the system.     

Chaotic synchronization: a nonlinear predictive filtering approach

The synchronization of chaotic systems is a difficult task due to their sensitive dependence on the initial conditions. Perfect synchronization is almost impossible when noise is present in the system. One of the well known stochastic filtering algorithms that is used to synchronize chaotic systems in the presence of noise is the extended Kalman filter (EKF). However, for highly nonlinear systems, the approximation error introduced by the EKF has been shown to be relatively high. In this paper, a nonlinear predictive filter (NPF) is proposed for synchronizing chaotic systems. In this scheme, it is not required to approximate the underlying nonlinearity and hence there is no need to compute the Jacobian of the chaotic system. Numerical simulations are carried out to compare the performances of the NPF and EKF algorithms for synchronizing different sets of chaotic systems and/or maps. The well known Lorenz and Mackey-Glass systems as well as Ikeda map are used for numerical evaluation of the performance. Results clearly show that the NPF based approach is superior to the EKF based approach in terms of the normalized mean square error (NMSE), total NMSE, and the time taken for synchronization (measured in terms of the normalized instantaneous square error) for all the systems and/or maps considered.     

Synchronization Control of Two Different Chaotic Systems with Known and Unknown Parameters

Chaos synchronization of two different chaotic systems with known and unknown parameters is studied. Based on the Lyapunov stability theory, two different chaotic systems with known parameters realize global synchronization via the successfully designed nonlinear controller. By employing an adaptive synchronization scheme, the synchronization of two different chaotic systems with unknown parameters is achieved. Numerical simulations validate the effectiveness of the theoretical analysis.     

Chaotic behaviours and control of chaos in the p-Ge photoconductor

The chaotic behaviours in the p--Ge photoconductor system are studied by changing the photo-excitation coefficient and the routes and parameter conditions are given for chaos generation in this system. A scheme for controlling chaos in the p--Ge photoconductor is presented by adding an ac bias current. Numerical simulations show that this scheme can be effectively used to control chaotic states into stable period states for this system. Moreover, the different period states with different period numbers can be obtained by appropriately adjusting the amplitude, frequency, and initial phase of the additional ac current.     

Chaotic synchronization of coupled ergodic maps

With few exceptions, studies of chaotic synchronization have focused on dissipative chaos. Though less well known, chaotic systems that lack dissipation may also synchronize. Motivated by an application in communication systems, we couple a family of ergodic maps on the N-torus and study the global stability of the synchronous state. While most trajectories synchronize at some time, there is a measure zero set that never synchronizes. We give explicit examples of these asynchronous orbits in dimensions two and four. On more typical trajectories, the synchronization error reaches arbitrarily small values and, in practice, converges. In dimension two we derive bounds on the average synchronization time for trajectories resulting from randomly chosen initial conditions. Numerical experiments suggest similar bounds exist in higher dimensions as well. Adding noise to the coupling signal destroys the invariance of the synchronous state and causes typical trajectories to desynchronize. We propose a modification of the standard coupling scheme that corrects this problem resulting in robust synchronization in the presence of noise.