Chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity

In this Letter, the concept of practical synchronization is introduced and the chaos synchronization of uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity is investigated. Based on the time-domain approach, a tracking control is proposed to realize chaos synchronization for the uncertain Genesio-Tesi chaotic systems with deadzone nonlinearity. Moreover, the guaranteed exponential convergence rate and convergence radius can be pre-specified. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the obtained result.     

Adaptive synchronization of hyperchaotic systems via passivity feedback control with time-varying gains

A passivity feedback control scheme with time-varying gains is proposed for adaptive synchronization of hyperchaotic systems. By transforming the synchronization error dynamics into an equivalent passive system, a synchronization control law with time-varying gains is achieved and the convergence of the synchronization errors is guaranteed. The feasibility and effectiveness of the proposed scheme is demonstrated through its application to hyperchaotic Lü systems.     

Genesio-Tesi和Coullet混沌系统之间的非线性反馈同步

分析了Genesio-Tesi 系统和Coullet系统的特性，表明两系统拓扑不等价但奇异吸引子结构具有一定相似性，而且采用非线性反馈控制方法实现了两系统之间的混沌同步.根据系统 的稳定性理论，得到了非线性反馈控制器的结构和反馈控制增益的取值范围.数值仿真的结 果表明理论分析的正确性. 关键词： 非线性反馈控制 Genesio-Tesi系统 Coullet系统 混沌同步     

Inverse synchronization of coupled fractional-order systems through open-plus-closed-loop control

In this paper, the inverse synchronization problem of fractional-order dynamical systems is investigated. A general explicit coupling via an open-plus-closed-loop control for inverse synchronization of two arbitrary unidirectionally or bidirectionally coupled fractional-order systems is proposed. The inverse synchronization is proved analytically based on the stability theorem of the fractional differential equations. A key feature of this proposed scheme is that it can be applied not only to nonchaotic but also to chaotic fractional-order systems whenever they exhibit regular or irregular oscillations. Feasibility of the proposed inverse synchronization scheme is illustrated through numerical simulations.     

Stabilization and synchronization of Genesio-Tesi system via single variable feedback controller

This Letter investigates the stabilization and synchronization of Genesio-Tesi systems. Firstly, modifying the previous method, we stabilize the Genesio-Tesi system. Then, we synchronize two identical Genesio chaotic system by extending the obtained stabilization results. To the best of our knowledge, the above controllers obtained in this Letter are simpler than those obtained in the existing results. Finally, numerical simulations verify the effectiveness and the validity of the above theoretical results.     

Impulsive control for synchronization of nonlinear Rossler chaotic systems

This paper reports that an impulsive control theory for synchronization of nonlinear R?ssler chaotic systems is developed. A new framework for impulsive synchronization between such chaotic systems is presented, which makes the synchronization error system a linear impulsive control system. Therefore, it is easy to derive the impulsive synchronization law. The proposed impulsive control scheme is illustrated by nonlinear R?ssler chaotic systems and the simulation results demonstrate the effectiveness of the method.     

Synchronization of impulsively coupled complex systems with delay

This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.     

Stability criterion for synchronization of chaotic systems using linear feedback control

This Letter introduces linear balanced feedback control scheme to design controller for the synchronization of two identical chaotic systems based on Lyapunov stability theory and constrained extreme approach. The technique is applied to synchronizing two identical four-scroll chaotic systems and guiding balanced feedback gains design. In accordance with the result of the analysis, an adaptive control scheme is proposed for chaos synchronization when the parametric variations of the response system are uncertain. The feasibility and effectiveness of the proposed synchronization scheme are verified via numerical simulations.     

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.     

On Impulsive Control for Synchronization and Its Application to Matsumoto-Chua-Kobayashi (MCK) Circuit

The issue of impulsive control theory for synchronization of the MCK circuit is developed. We propose an impulsive control scheme for the complete synchronization of the MCK circuit including chaotic systems. A sufficient condition for the impulsive control is derived, with an easily calculated maximum impulsive interval. The proposed impulsive control scheme is applied to the MCK circuit and the simulation result demonstrates the effectiveness of the method.     

On Impulsive Control for Synchronization and Its Application to Matsumoto-Chua-Kobayashi （MCK） Circuit

The issue of impulsive control theory for synchronization of the MCK circuit is developed. We propose an impulsive control scheme for the complete synchronization of the MCK circuit including chaotic systems. A sufficient condition for the impulsive control is derived, with an easily calculated maximum impulsive interval. The proposed impulsive control scheme is applied to the MCK circuit and the simulation result demonstrates the effectiveness of the method.     

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.     

统一混沌系统的投影同步与控制

对单向耦合的统一混沌系统间的投影同步进行了研究与控制-分析了投影同步现象的产生机 理，给出一方案对投影同步的特征量进行控制-该方案所需控制代价较小, 为设计适当的混 沌信号源提供了一种理论依据，在利用混沌电路系统进行保密通信方面有着一定的应用前景 -仿真实例表明理论分析的正确性和实际控制方案的有效性- 关键词： 统一混沌系统 投影同步 混沌控制 单向耦合     

Impulsive control for synchronization of a class of continuous systems

An impulsive control theory for synchronization of a class of continuous systems is developed. A sufficient condition for the impulsive control is derived. The proposed impulsive control scheme is illustrated by some continuous chaotic systems and the simulation results demonstrate the effectiveness of the method.     

Synchronization of fractional-order chaotic systems with non-identical orders,unknown parameters and disturbances via sliding mode control

The scheme of synchronization between fractional-order chaotic systems with non-identical orders, unknown parameters and disturbances was investigated. A sliding surface was defined based on the theory of sliding mode control and a controller with adaptive laws was designed based on the stability of fractional-order nonlinear systems. The synchronization of two fractional-order hyperchaotic systems was simulated by using the fractional differential transform method to validate the effectiveness and the feasibility of the proposed scheme. All the theoretical analysis and simulation results showed the effectiveness of the proposed scheme.     

A new scheme to generalized (lag, anticipated, and complete) synchronization in chaotic and hyperchaotic systems

In this paper, a generalized (lag, anticipated, and complete) synchronization of a class of continuous-time systems is defined. A systematic, powerful and concrete scheme is developed to investigate the generalized (lag, anticipated, and complete) synchronization between the drive system and response system based on the active control idea. The hyperchaotic R?ssler system, transformed R?ssler and Chen system as well as two coupled nonidentical R?ssler oscillators are chosen to illustrate the proposed scheme. Numerical simulations are used to verify the effectiveness of the proposed scheme. The scheme can be also extended to research generalized (lag, anticipated, and complete) synchronization between other dynamical systems.     

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.     

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.     

Finite-time sliding mode synchronization of chaotic systems

A new finite-time sliding mode control approach is presented for synchronizing two different topological structure chaotic systems. With the help of the Lyapunov method, the convergence property of the proposed control strategy is discussed in a rigorous manner. Furthermore, it is mathematically proved that our control strategy has a faster convergence speed than the conventional finite-time sliding mode control scheme. In addition, the proposed control strategy can ensure the finite-time synchronization between the master and the slave chaotic systems under internal uncertainties and external disturbances. Simulation results are provided to show the speediness and robustness of the proposed scheme. It is worth noticing that the proposed control scheme is applicable for secure communications.     

Synchronization of impulsively coupled complex networks

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete instants.Based on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve synchronization.The proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the network.In addition,it is unnecessary for the impulsive coupling matrix to be symmetrical.Finally,the proposed control scheme is applied to a chaotic Lorenz network and Chua’s circuit network.Numerical simulations are used to illustrate the validity of this control scheme.