Adaptive Modified Function Projective Synchronization Research Articles

Control and adaptive modified function projective synchronization of a new chaotic system

Control and adaptive modified function projective synchronization of a new chaotic system

Control and adaptive modified function projective synchronization of different hyperchaotic dynamical systems

<abstract><p>In this work, we consider an adaptive control method, which is simpler and generalized to obtain some conditions on the parameters for hyperchaotic models determined by using a Lyapunov direct method. Further, an adaptive controller for synchronization is designed by using Lyapunov functions by which the deriving system and the response system can realize adaptive modified function projective synchronization up to scaling matrix. Numerical simulation of each system is discussed in detail with graphical results. The graphical results are presented in detail in order to validate the theoretical results. These results in this article generalize and improve the corresponding results of the recent works.</p></abstract>

Control and adaptive modified function projective synchronization of a new hyperchaotic system

The purpose of this investigation is the applications of the feedback control method in order to control the behavior of the new hyperchaotic system. We consider hyperchaotic system first and then apply the feedback control method to obtain the results for the control of the hyperchaotic system. We present some conditions on the parameters values and show that the controlled system is stable which is established by the Routh–Hurwitz criterion. We also show results for the adaptive modified function projective synchronization (AMFPS) of two identical new hyperchaotic systems with known parameters. Using the Lyapunov stability theory, we can present the system that the is asymptotically stable. At last, we provide numerical results for the justifications of the theoretical results by considering the initial values of the variables and the suitable parameters values. The simulated results justify the importance of the considered method.

Adaptive Modified Function Projective Synchronization for Uncertain Complex Dynamic Networks With Multiple Time-Varying Delay Couplings Under Input Nonlinearity

This paper is concerned with the modified function projective synchronization of the uncertain complex dynamic networks with both input nonlinearity and multiple time-varying delay couplings. Firstly, the model of the complex dynamic networks with sector nonlinear input, multiple time-varying delay couplings, model uncertainty and external disturbance is constructed. Then, the adaptive controller is formulated based on the Lyapunov stability theory and the matrix inequality theory, by which the network nodes of the driving system and the response system can realize modified function projective synchronization according to the corresponding function scaling factors. Finally, a four-dimensional hyperchaotic system is considered as the nodes of the complex dynamic networks to achieve numerical simulation. The corresponding theoretical proof and computer simulation are worked out to demonstrate the effectiveness and feasibility of the proposed scheme.

Adaptive Modified Function Projective Synchronization of Uncertain Complex Dynamical Networks with Multiple Time-Delay Couplings and Disturbances

This paper studies the modified function projective synchronization of uncertain complex dynamic network model with multiple time-delay couplings and external disturbances. Based on Lyapunov stability theory, the positive definite function is designed and the sufficient conditions of synchronization are given. Both the uncertain parameters and the unknown bounded disturbances are estimated in accordance with the adaptive laws. With the adaptive feedback controller, the complex dynamic network can synchronize with reference node by a scaling function matrix. The reference node can be periodic orbit, equilibrium point, or a chaotic attractor. Finally, two numerical simulations are offered to illustrate the effectiveness of the proposed method.

Modified function projective feedback control for time-delay chaotic Liu system synchronization and its application to secure image transmission

This paper is devoted to synchronize time-delay Liu chaotic system in order to develop a secure image transmission system. An adaptive modified function projective synchronization (MFPS) method is proposed to control the behavior of the uncertain Liu chaotic system in the presence of time-delay state variables and uncertainty in system parameters. The stability and convergence of the present method are analyzed by means of Lyapunov stability theorem. Numerical simulations were used to validate the effectiveness of the proposed MFPS method. Furthermore, a novel image cryptosystem is generated for secure image transmission. Image data is embedded within the response signals and is transmitted to the receiver. The image data can be extracted at the receiver by using of the drive signals. The proposed image cryptosystem was applied to a plain image, and also, performance of the image cryptosystem was evaluated by some mathematical tools and the results were satisfactory, in both cases.

Adaptive modified function projective synchronization of general uncertain chaotic complex systems

This paper discusses the modified function projective synchronization (MFPS) of general chaotic complex systems described by a unified mathematical expression. Based on the Lyapunov stability theory, an adaptive controller is designed to synchronize two general uncertain chaotic complex systems in the sense of MFPS and some parameter update laws for estimating unknown parameters of the systems are also given. Moreover, the control coefficients can be automatically adapted to updated laws. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

Adaptive modified function projective synchronization of a class of chaotic systems with uncertainties

In this paper, we primarily investigate the adaptive modifying function projective synchronization of a class of chaotic systems with uncertainties. According to the Lyapunov stability theory, the two schemes of obtaining the response system from chaotic system are established, and the controller and the adaptive law are designed. The approach is more robust to noise and external interference, and does not need the upper bound of uncertainties in advance. In addition, it can adjust the system response rapidly by adjusting the accelerated factor. This method is more practical. Numerical simulations of a hyper-chaotic system verify the effectiveness of the proposed method.

Adaptive Modified Function Projective Synchronization between Two Different Hyperchaotic Dynamical Systems

This work investigates modified function projective synchronization between two different hyperchaotic dynamical systems, namely, hyperchaotic Lorenz system and hyperchaotic Chen system with fully unknown parameters. Based on Lyapunov stability theory, the adaptive control law and the parameter update law are derived to achieve modified function projective synchronized between two diffierent hyperchaotic dynamical systems. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

Adaptive modified function projective synchronization of unknown chaotic systems with different order

This paper investigates the modified function projective synchronization (MFPS) between two different dimensional chaotic systems with fully unknown or partially unknown parameters via increased order. Based on the Lyapunov stability theorem and adaptive control method, a unified adaptive controller and parameters update law can be designed for achieving the MFPS of the two different chaotic systems with different orders. Numerical simulations are presented to show the effectiveness of the proposed synchronization scheme.

Adaptive modified function projective synchronization and parameter identification of uncertain hyperchaotic (chaotic) systems with identical or non-identical structures

Modified function projective synchronization (MFPS), which generalizes many kinds of synchronization form, has received great attention recently. Based on the active control method and adaptive control technique, a general formula for designing the controllers is proposed to achieve adaptive MFPS, which corrects several incomplete results that have been reported recently. In addition, this paper derives the sufficient condition for parameter identification, which was not mentioned in much of the relevant literature concerning MFPS. Furthermore, we extend the MFPS scheme to the cases that the drive and response systems come with non-identical structures. The proposed method is both theoretically rigorous and practically feasible, which has the merits that it can not only achieve the full-state MFPS but also identify the fully unknown parameters in the synchronization process. The theoretical results are successfully applied to three typical illustrative cases: the adaptive MFPS of two identical 4-D hyperchaotic systems with unknown parameters in the response system, the adaptive MFPS between a 5-D hyperchaotic system and a 4-D hyperchaotic system with unknown parameters in the drive system and the adaptive MFPS between a 3-D chaotic system and a 4-D hyperchaotic system when the parameters in the drive system and response system are all unknown. For each case the controller functions and parameter update laws are well designed in detail. Moreover, the corresponding numerical simulations are presented, which agree well with the theoretical analysis.

Robust adaptive modified function projective synchronization of different hyperchaotic systems subject to external disturbance

Robust adaptive modified function projective synchronization between two different hyperchaotic systems is investigated, where the external uncertainties are considered and the scale factors are different from each other. The synchronization criterion is presented, which can be realized by adaptive feedback controller with compensator to eliminate the influence of uncertainties effectively. The update laws of the unknown parameters are given and the sufficient conditions are deduced based on stability theory and adaptive control. And some mistakes in the previous works are pointed out and revised. Finally, the hyperchaotic Lü and new hyperchaotic Lorenz systems are taken for example and the numerical simulations are presented to verify the effectiveness and robustness of the proposed control scheme.

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.

Adaptive modified function projective synchronization of different hyperchaotic systems

This article treats the modified function projective synchronization between the hyperchaotic Lorenz-Stenflo(LS) system and a novel hyperchaotic CYQY system, and also that between the LS system and hyperchaotic Chen system, which have completely unknown parameters. By utilizing Lyapunov stability theory and active control method, the adaptive controllers and parameter update laws are derived to make the states of different hyperchaotic systems to attain adaptive modified function projective synchronization. The systems unknown parameters can be identified simultaneously. Numerical simulations are presented to demonstrate the effectiveness of the proposed methods.

Adaptive modified function projective synchronization of hyperchaotic systems with unknown parameters

This paper is involved with the adaptive modified function projective synchronization (MFPS) problem of hyperchaotic systems with unknown parameters. Based on the Lyapunov stability theorem and adaptive control method, adaptive controllers and parameters update laws can be presented for the MFPS not only between two identical hyperchaotic systems but particularly also between two different hyperchaotic systems with fully unknown or partially unknown parameters. Moreover, the coupling strength can be automatically adapted to a updated law. Numerical simulations are presented to show the effectiveness of the proposed synchronization schemes.

Adaptive modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system with uncertain parameters

This Letter investigates modified function projective synchronization between hyperchaotic Lorenz system and hyperchaotic Lu system using adaptive method. By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two hyperchaotic systems modified function projective synchronized. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.