Adaptive anti-synchronization of two identical and different hyperchaotic systems with uncertain parameters

This paper brings attention to hyperchaos anti-synchronization between two identical and different hyperchaotic systems by using adaptive control. The sufficient conditions for achieving the anti-synchronization of two hyperchaotic systems are derived based on Lyapunov stability theory. An adaptive control law and a parameter update rule for unknown parameters are introduced such that the hyperchaotic Chen system is controlled to be the hyperchaotic Lü system. Theoretical analysis and numerical simulations are shown to verify the results.     

Adaptive synchronization between two different hyperchaotic systems

This work presents chaos synchronization between two different hyperchaotic systems using adaptive control. The sufficient conditions for achieving synchronization of two high dimensional chaotic systems are derived based on Lyapunov stability theory, and an adaptive control law and a parameter update rule for unknown parameters are given such that generalized Henon–Heiles system is controlled to be hyperchaotic Chen system. Theoretical analysis and numerical simulations are shown to verify the results.     

Chaos synchronization of a new hyperchaotic system

In this paper, two kinds of synchronization schemes for a new hyperchaotic system are presented. Firstly, on the basis of stability criterion of linear system, synchronization is achieved with the help of the active control theory. Secondly, a nonlinear controller is designed according to Lyapunov stability theory to assure that synchronization can be achieved. Furthermore, an adaptive control approach for synchronization of uncertain hyperchaotic systems is proposed. Finally numerical simulations are provided to show the effectiveness and feasibility of the developed methods.     

Achieving synchronization between the fractional-order hyperchaotic Novel and Chen systems via a new nonlinear control technique

In this work, we discuss the stability conditions for a nonlinear fractional-order hyperchaotic system. The fractional-order hyperchaotic Novel and Chen systems are introduced. The existence and uniqueness of solutions for two classes of fractional-order hyperchaotic Novel and Chen systems are investigated. On the basis of the stability conditions for nonlinear fractional-order hyperchaotic systems, we study synchronization between the proposed systems by using a new nonlinear control technique. The states of the fractional-order hyperchaotic Novel system are used to control the states of the fractional-order hyperchaotic Chen system. Numerical simulations are used to show the effectiveness of the proposed synchronization scheme.     

Adaptive synchronization of a hyperchaotic system with uncertain parameter

This paper addresses the synchronization problem of two Lü hyperchaotic dynamical systems in the presence of unknown system parameters. Based on Lyapunov stability theory an adaptive control law is derived to make the states of two identical Lü hyperchaotic systems with unknown system parameters asymptotically synchronized. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization schemes.     

Secure communications based on the synchronization of the hyperchaotic Chen and the unified chaotic systems

This paper deals with the adaptive synchronization of two identical hyperchaotic master and slave systems. The master system and the slave system each consists of two subsystems: a hyperchaotic Chen subsystem and a unified chaotic subsystem. The asymptotic convergence of the errors between the states of the master system and the states of the slave system is proven using Lyapunov theory. Simulation results are presented to illustrate the ability of the control law to synchronize the master and slave systems. Moreover, the proposed control scheme is applied to encrypt and decrypt discrete signals such as digital images where computer simulation results are provided to show that the proposed control law works well.     

Hyperchaotic secure communication via generalized function projective synchronization

This paper presents two different hyperchaotic secure communication schemes by using generalized function projective synchronization (GFPS), where the drive and response systems could be synchronized up to a desired scaling function matrix. The unpredictability of the scaling functions can additionally enhance the security of communication. First, a hyperchaotic secure communication scheme applying GFPS of the uncertain Chen hyperchaotic system is proposed. The transmitted information signal is modulated into the parameter of the Chen hyperchaotic system in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical Chen hyperchaotic systems with unknown parameter asymptotically synchronized; thus, the uncertain parameter of the receiver system is identified. The information signal can be recovered accurately by the estimated parameter. Secondly, another secure communication scheme by the coupled GFPS of the Chen hyperchaotic system is introduced. The information signal transmitted can be extracted exactly through simple operation in the receiver. The corresponding theoretical proofs and numerical simulations demonstrate the validity and feasibility of the proposed hyperchaotic secure communication schemes.     

Switched modified function projective synchronization of hyperchaotic Qi system with uncertain parameters

This work is involved with switched modified function projective synchronization of two identical Qi hyperchaotic systems using adaptive control method. Switched synchronization of chaotic systems in which a state variable of the drive system synchronize with a different state variable of the response system is a promising type of synchronization as it provides greater security in secure communication. Modified function projective synchronization with the unpredictability of scaling functions can enhance security. Recently formulated hyperchaotic Qi system in the hyperchaotic mode has an extremely broad frequency bandwidth of high magnitudes, verifying its unusual random nature and indicating its great potential for some relevant engineering applications such as secure communications. By Lyapunove stability theory, the adaptive control law and the parameter update law are derived to make the state of two chaotic systems modified function projective synchronized. Synchronization under the effect of noise is also considered. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.     

Chaos synchronization between two novel different hyperchaotic systems with unknown parameters

This work is devoted to investigating the synchronization between two novel different hyperchaotic systems with fully unknown parameters, i.e., an uncertain hyperchaotic Lorenz system and an uncertain hyperchaotic Lü system. Based on the Lyapunov stability theory, a new adaptive controller with parameter update law is designed to synchronize these two hyperchaotic systems asymptotically and globally. Numerical simulations are presented to verify the effectiveness of the synchronization scheme.     

Modified projective synchronization of uncertain fractional order hyperchaotic systems

Base on the stability theory of fractional order system, this work mainly investigates modified projective synchronization of two fractional order hyperchaotic systems with unknown parameters. A controller is designed for synchronization of two different fractional order hyperchaotic systems. The method is successfully applied to modified projective synchronization between fractional order Rössler hyperchaotic system and fractional order Chen hyperchaotic system, and numerical simulations illustrate the effectiveness of the obtained results.     

Synchronization and anti-synchronization of a hyperchaotic Chen system

Based on the active control theory, synchronization and anti-synchronization between two identical chaotic systems is investigated. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. Through rigorous mathematical theory, the sufficient condition is drawn for the stability of the error dynamics, where the controllers are designed by using the sum of the relevant variables in chaotic systems. Numerical simulations are performed for Chen hyperchaotic dynamical system to demonstrate the effectiveness of the proposed control strategy.     

Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances

In this paper, we demonstrate that anti-synchronization can coexist in two different hyperchaotic systems with terms of parametric uncertainty and external disturbances using the robust active sliding mode control method. By using rigorous mathematical theory, the sufficient condition is drawn for the stability of error dynamics based on the Lyapunov stability theory, where the controllers are designed by using the sum of the relevant variables in hyperchaotic systems. Numerical results are presented to justify the theoretical analysis.     

Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters

This paper addresses problems of control and synchronization for a new modified hyperchaotic Lü system with uncertain parameters. This new modified uncertain hyperchaotic Lü system is stabilized to its unique unstable equilibrium by using adaptive control. Furthermore, an adaptive control law and a parameter estimation update law are derived to synchronize two identical modified hyperchaotic Lü systems with uncertain parameters. Numerical examples are proposed to demonstrate and verify the theoretical analysis.     

Synchronization of hyperchaotic systems via linear control

In this paper, synchronization of hyperchaotic system is discussed. Based on the stability theory in the cascade system, a simple linear feedback law is presented to realize synchronization of hyperchaotic systems. Simulation results are given to illustrate the effectiveness of the proposed method.     

Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters

This paper investigates adaptive synchronization between two novel different hyperchaotic systems with partly uncertain parameters. Based on the Lyapunov stability theorem and the adaptive control theory, synchronization between these two hyperchaotic systems is achieved by proposing a new adaptive controller and a parameter estimation update law. Numerical simulations are presented to demonstrate the analytical results.     

Synchronization of two hyperchaotic systems via adaptive control

This letter presents chaos synchronization problem of two different hyperchaotic systems when the parameters of drive and response systems are fully unknown or uncertain. Based on Lyapunov stability theory, an adaptive control law and a parameter update rule for unknown parameters are derived such that two different high dimensional chaotic systems are to be synchronized. Hyperchaotic Chen system and Second-harmonic generation (SHG) system are taken as an illustrative example to show the effectiveness of the proposed method.     

Control and synchronize a novel hyperchaotic system

The control and hybrid projective synchronization (HPS) strategies for a novel hyperchaotic system are investigated. Firstly, the novel hyperchaotic system is controlled to the unsteady equilibrium point or limit cycle via only one scalar controller which includes two state variables. Secondly, based on Lyapunov’s direct method HPS between two novel hyperchaotic systems is studied. A new nonlinear feedback vector controller is designed to guarantee HPS, which can be simplified ulteriorly into a single scalar controller to achieve complete synchronization between two novel hyperchaotic systems. Finally, numerical simulations are given to verify the effectiveness of these strategies. The proposed methods have certain significances for reducing the cost and complexity for controller implementation.     

Ultimate bound sets of a hyperchaotic system and its application in chaos synchronization

In this article, we investigate globally exponentially attractive sets and chaos synchronization for a hyperchaotic system, namely, Lorenz–Stenflo system. For this system, two ellipsoidal globally exponentially attractive sets are derived based on generalized Lyapunov function theory and the extremum principle of function. Furthermore, we propose linear feedback control with a one, two, three, and four inputs to realize globally exponential synchronization of two four‐dimesional hyperchaotic systems using inequality techniques. Numerical simulations are presented to show the effectiveness of the proposed synchronization scheme. © 2014 Wiley Periodicals, Inc. Complexity 20: 30–44, 2015     

Control of a novel fractional hyperchaotic system using a located control method

Fractional order dynamics and chaotics systems have been recently combined, yielding interesting behaviours. In this paper, a novel integer order hyperchaotic system is considered. Then, a fractional order hyperchaotic representation of said system is proposed using a natural fractionalization. Two different linear control methodologies to deal with the complexity which introduce such systems are proposed. Those methods are able to modify the hyperchaotic behaviour of the system and force it to move towards a fixed point; i.e. steady state. These approaches give a general framework for taming such complex systems using simple linear controllers. The main tools for analysing the controlled system are Matignon stability criterion and RouthHurwitz test. Using a reliable numerical simulation, the designed system is simulated to verify the theoretical analysis.     

Anti-synchronization in two non-identical hyperchaotic systems with known or unknown parameters

This paper considers the anti-synchronization problem between hyperchaotic Rössler system and hyperchaotic Lorenz system. Two anti-synchronization schemes of them are proposed. Active control is applied when system parameters are known and adaptive control is employed when system parameters are unknown or uncertain. Controllers and update laws of parameters are designed based on Lyapunov stability theory. In both cases, sufficient conditions for the anti-synchronization are obtained analytically. Finally, numerical simulations are provided to show the effectiveness of the proposed schemes.