Modified Function Projective Synchronization Research Articles

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 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 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 OPEN-PLUS-CLOSED-LOOP CONTROL METHOD OF MODIFIED FUNCTION PROJECTIVE SYNCHRONIZATION IN COMPLEX NETWORKS

This paper investigates the modified function projective synchronization (MFPS) in drive-response dynamical networks (DRDNs) with different nodes, which means that systems in nodes are strictly different. An adaptive open-plus-closed-loop (AOPCL) control method is proposed, which is a practically realizable method and can overcome the model mismatched to achieve synchronization. It is well known that each of the close-loop and open-loop control method possesses some advantages and disadvantages. By combining their advantages, the open-plus-closed-loop (OPCL) control method was proposed by Jackson and Grosu. For arbitrary nonlinear dynamic systems, dx/dt = F(x,t), Jackson and Grosu proved that there exists solutions, x(t), in the neighborhood of any arbitrary goal dynamics g(t) that are entrained to g(t), through the use of an additive controlling action, K(g,x,t) = H(dg/dt,g) + C(g,t)(g(t) - x), which is the sum of the open-loop action, H(dg/dt,g), and a suitable linear closed-loop (feedback) action C(g,t). This method is a practically realizable method and robust to limited accuracy of data and effects of noise. The AOPCL control method preserve the merits of OPCL control method and its closed loop control part can be automatically adapted to suitable constants. Considering time-delays are always unavoidably in the practical situations, MFPS in DRDNs with time-varying coupling delayed is further investigated by the proposed method. Corresponding numerical simulations are performed to verify and illustrate the analytical results.

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.

MODIFIED FUNCTION PROJECTIVE SYNCHRONIZATION OF CHAOTIC NEURAL NETWORKS WITH DELAYS BASED ON OBSERVER

This paper deals with a new type of synchronization scheme for chaotic neural networks with delays, called modified function projective synchronization, in which chaotic neural networks synchronize up to a scaling function matrix. Based on the nonlinear state observer, a control scheme is derived through the placement technique by designing a state-observer of the derived system to synchronize chaotic neural networks up to a scaling function matrix. This technique, capable of adjusting the scaling function factor arbitrarily for the value of scaling function factor, has no effect on the controllability of error system. That overcomes some limitation in earlier literature. A chaotic cellular neural network and a chaotic Hopfield neural model are used as numerical examples to demonstrate the effectiveness of the proposed synchronization technique.

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.

Modified function projective synchronization of a class of chaotic systems

A general method of modifying function projective synchronization of a class of chaotic systems is proposed in this paper by designing a suitable response system. The two schemes of obtaining the response system from chaotic system are established based on unidirectional coupled synchronization. Since chaos synchronization can be achieved by transmitting only a single variable from driving system to response system, this method is more practical. The stability analysis in the paper is proved using Lyapunov stability theory. Numerical simulations of a hyperchaotic system verify the effectiveness of the proposed method.

Modified function projective synchronization of hyperchaotic systems through Open-Plus-Closed-Loop coupling

Recently introduced modified function projective synchronization (MFPS) in which chaotic systems synchronize up to a scaling function matrix has important applications in secure communications. We design coupling function for unidirectional coupling in identical and mismatched hyperchaotic oscillators to realize MFPS through Open-Plus-Closed-Loop (OPCL) coupling method. The arbitrary scaling function matrix elements are properly chosen such that we can produce function projective synchronization, synchronization, anti-synchronization and amplitude death on desired states of the response system simultaneously. Numerical simulations on identical hyperchaotic Rossler and mismatched hyperchaotic Lu system are presented to verify the effectiveness of the proposed scheme. A secure communication scheme based on MFPS is also presented.

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.

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.

Modified function projective synchronization of chaotic system

This paper presents a new type synchronization called modified function projective synchronization, where the drive and response systems could be synchronized up to a desired scale function matrix. It is obvious that the unpredictability of the scaling functions can additionally enhance the security of communication. By active control scheme, we take Lorenz system as an example to illustrate above synchronization phenomenon. Furthermore, based on modified function projective synchronization, a scheme for secure communication is investigated in theory. The corresponding numerical simulations are performed to verify and illustrate the analytical results.