Multiswitching compound antisynchronization of four chaotic systems

Based on three drive–one response system, in this article, the authors investigate a novel synchronization scheme for a class of chaotic systems. The new scheme, multiswitching compound antisynchronization (MSCoAS), is a notable extension of the earlier multiswitching schemes concerning only one drive–one response system model. The concept of multiswitching synchronization is extended to compound synchronization scheme such that the state variables of three drive systems antisynchronize with different state variables of the response system, simultaneously. The study involving multiswitching of three drive systems and one response system is first of its kind. Various switched modified function projective antisynchronization schemes are obtained as special cases of MSCoAS, for a suitable choice of scaling factors. Using suitable controllers and Lyapunov stability theory, sufficient condition is obtained to achieve MSCoAS between four chaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed using Lorenz system in MATLAB to demonstrate the validity of the presented method.     

A new output feedback synchronization theorem for a class of chaotic systems with a scalar transmitted signal

This paper proposes a new, simple and yet applicable output feedback synchronization theorem for a large class of chaotic systems. We take a linear combination of drive system state variables as a scale-driving signal. It is proved that synchronization between the drive and the response systems can be obtained via a simple linear output error feedback control. The linear feedback gain is a function of a free parameter. The approach is illustrated using the R\"{o}ssler hyperchaotic systems and Chua's chaotic oscillators.     

Multiswitching combination–combination synchronization of chaotic systems

In this paper, a novel synchronization scheme is investigated for a class of chaotic systems. The multiswitching synchronization scheme is extended to the combination–combination synchronization scheme such that the combination of state variables of two drive systems synchronize with different combination of state variables of two response systems, simultaneously. The new scheme, multiswitching combination–combination synchronization (MSCCS), is a notable extension of the earlier multiswitching schemes concerning only the single drive–response system model. Various multiswitching modified projective synchronization schemes are obtained as special cases of MSCCS, for a suitable choice of scaling factors. Suitable controllers have been designed and using Lyapunov stability theory sufficient condition is obtained to achieve MSCCS between four hyperchaotic systems and the corresponding theoretical proof is given. Numerical simulations are performed to validate the theoretical results.     

Multi-switching dual compound synchronization of chaotic systems

A novel multi-switching dual compound synchronization scheme is proposed for chaotic systems which has not been investigated so far. The goal is to design appropriate controllers by using Lyapunov stability theory and nonlinear control to establish the asymptotically stable synchronized state for six drive and two response systems. Multi-switching dual compound synchronization can be considered as an extension of multi-switching dual combination synchronization. An example is presented to elaborate the proposed scheme where Lorenz, Chen, Lu systems are considered as master systems and T system is considered as slave system. The results obtained by theoretical and graphical analysis are in excellent agreement.     

Arbitrary full-state hybrid projective synchronization for chaotic discrete-time systems via a scalar signal

In this paper we present a new projective synchronization scheme,where two chaotic(hyperchaotic) discretetime systems synchronize for any arbitrary scaling matrix.Specifically,each drive system state synchronizes with a linear combination of response system states.The proposed observer-based approach presents some useful features:i) it enables exact synchronization to be achieved in finite time(i.e.,dead-beat synchronization);ii) it exploits a scalar synchronizing signal;iii) it can be applied to a wide class of discrete-time chaotic(hyperchaotic) systems;iv) it includes,as a particular case,most of the synchronization types defined so far.An example is reported,which shows in detail that exact synchronization is effectively achieved in finite time,using a scalar synchronizing signal only,for any arbitrary scaling matrix.     

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     

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.     

Perfect synchronization of chaotic systems： a controllability perspective

This paper presents a synchronization method, motivated from the constructive controllability analysis, for two identical chaotic systems. This technique is applied to achieve perfect synchronization for Lorenz systems and coupled dynamo systems. It turns out that states of the drive system and the response system are synchronized within finite time, and the reaching time is independent of initial conditions, which can be specified in advance. In addition to the simultaneous synchronization, the response system is synchronized un-simultaneously to the drive system with different reaching time for each state. The performance of the resulting system is analytically quantified in the face of initial condition error, and with numerical experiments the proposed method is demonstrated to perform well.     

Globally exponential multi switching-combination synchronization control of chaotic systems for secure communications

This article introduces the global exponential multi switching combination synchronization (GEMSCS) for three different chaotic systems with known parameters in the master-slave system configuration. The proposed GEMSCS scheme establishes the global exponential stability of the synchronization error at the origin with different combinations of state variables of the two master chaotic systems with the state variables of a slave chaotic system in diverse manners. Consequently, it increases the complexity level of the information signal in secure communications. To study the GEMSCS, an efficient nonlinear control algorithm is designed. The Lyapunov direct theorem is used to accomplish the global exponential stability of the synchronization error at the origin. The stability conditions are derived analytically. To show the effectiveness and advantages of the proposed GEMSCS control approach, two numerical examples are presented. The computer based simulation results are compared with the reported works in the relevant literature. This article also extends the idea of GEMSCS to the secure communication using the chaotic masking technique. Using the GEMSCS strategy, the information signal is recovered at the receiving system with good accuracy and high speed while the parameters of the transmitter and receiver systems mismatch. At the end, some future research problems related to this work are suggested.     

一类关联混沌系统及其切换与内同步机理研究

提出了一类新的具有切换与内同步特性的关联混沌系统, 该系统即可在同维系统间切换, 也可在不同维系统间切换, 当系统切换为四维系统后, 还可实现系统变量间的同步. 通过理论推导、数值仿真、 Lyapunov维数、Lyapunov指数谱研究了其基本动力学特性与内同步机理. 最后, 设计了该切换混沌系统的硬件电路并运用Multisim软件对该混沌系 统及其内同步特性进行了仿真实现, 数值仿真和电路仿真证实了该切换混沌系统物理可实现, 系统具有丰富的动力学特性. 关键词： 关联混沌系统 Lyapunov指数 切换 内同步     

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors （CMPS） of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes.     

基于函数矩阵的一类混沌系统同步

研究了一类混沌系统的同步问题、基于稳定性理论和极点配置技术,设计了两个混沌系统之间的同步方案,实现两个混沌系统之间的同步,通过函数矩阵,实现驱动系统和响应系统的状态变量按给定的函数矩阵同步,同时证明了该方法同样适用于两个混沌系统之间的滞后同步,通过对Lorenz混沌系统和Lorenz超混沌系统的数值模拟,进一步验证了所提方案的有效性。     

INVERSE SYNCHRONIZATION OF CHAOTIC SYSTEMS IN AN ERBIUM-DOPED FIBRE DUAL-RING LASER USING THE MUTUAL COUPLING METHOD

Inverse synchronization of chaos is a type of synchronization in which the dynamical variables of two chaotic systems are inversely equal. In this paper, we present a scheme for inverse synchronization of two chaotic systems in an erbium-doped fibre dual-ring laser using the mutual coupling method. For realistic values of the systems, we demonstrate two kinds of results, as follows. (1) Two independent identical chaotic systems can go into inversely synchronized chaotic oscillation for coupling greater than 0.03. (2) When some parameter of one system varies, the state of the coupled systems could go into some periodic states directly or by inverse bifurcation. Simultaneously, they will lose the synchronization as the parameter changes.     

Robust Stabilization and Synchronization of a Novel Chaotic System with Input Saturation Constraints

In this paper, the robust stabilization and synchronization of a novel chaotic system are presented. First, a novel chaotic system is presented in which this system is realized by implementing a sigmoidal function to generate the chaotic behavior of this analyzed system. A bifurcation analysis is provided in which by varying three parameters of this chaotic system, the respective bifurcations plots are generated and evinced to analyze and verify when this system is in the stability region or in a chaotic regimen. Then, a robust controller is designed to drive the system variables from the chaotic regimen to stability so that these variables reach the equilibrium point in finite time. The robust controller is obtained by selecting an appropriate robust control Lyapunov function to obtain the resulting control law. For synchronization purposes, the novel chaotic system designed in this study is used as a drive and response system, considering that the error variable is implemented in a robust control Lyapunov function to drive this error variable to zero in finite time. In the control law design for stabilization and synchronization purposes, an extra state is provided to ensure that the saturated input sector condition must be mathematically tractable. A numerical experiment and simulation results are evinced, along with the respective discussion and conclusion.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs. Based on the adaptive technique, sliding mode control method and pole assignment technique, a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

Adaptive projective synchronization of different chaotic systems with nonlinearity inputs

We investigate the projective synchronization of different chaotic systems with nonlinearity inputs.Based on the adaptive technique,sliding mode control method and pole assignment technique,a novel adaptive projective synchronization scheme is proposed to ensure the drive system and the response system with nonlinearity inputs can be rapidly synchronized up to the given scaling factor.     

基于鲁棒有限时控制的混沌系统的同步

通过构造快速滑模控制器，实现了混沌系统的有限时同步，指出许多混沌系统经过状态变换后，都可以通过快速收敛的有限时控制器在有限时间内实现驱动系统和响应系统的完全同步，并以陈氏混沌系统和四阶细胞神经网络超混沌系统为例进行了系统仿真.结果显示，该有限时控制器不仅具有良好的性能，而且具备较强的鲁棒性. 关键词： 鲁棒控制 有限时同步 混沌系统     

Synchronization and parameter identification of one class of realistic chaotic circuit

In this paper, the synchronization and the parameter identification of the chaotic Pikovsky--Rabinovich (PR) circuits are investigated. The linear error of the second corresponding variables is used to change the driven chaotic PR circuit, and the complete synchronization of the two identical chaotic PR circuits is realized with feedback intensity k increasing to a certain threshold. The Lyapunov exponents of the chaotic PR circuits are calculated by using different feedback intensities and our results are confirmed. The case where the two chaotic PR circuits are not identical is also investigated. A general positive Lyapunov function V, which consists of all the errors of the corresponding variables and parameters and changeable gain coefficient, is constructed by using the Lyapunov stability theory to study the parameter identification and complete synchronization of two non-identical chaotic circuits. The controllers and the parameter observers could be obtained analytically only by simplifying the criterion dV/dt<0 (differential coefficient of Lyapunov function V with respect to time is negative). It is confirmed that the two non-identical chaotic PR circuits could still reach complete synchronization and all the unknown parameters in the drive system are estimated exactly within a short transient period.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

基于观测器的混沌广义同步解析设计

提出用改进的状态观测器研究混沌广义同步问题.采用解析法求得了混沌广义同步的响应系统.从状态观测器理论，得到驱动和响应系统全局渐进线性广义同步的充分条件.以超混沌R?ssler系统为例，数值研究了该同步方法.结果表明了它的有效性. 关键词： 混沌 广义同步 状态观测器 R?ssler系统