Projective Synchronization Method Research Articles

Finite-time function projective synchronization control method for chaotic wind power systems

Wind power is a rapidly growing renewable energy source that plays an increasingly important role in power systems. However, its dynamic behaviors are complex because of the instability of wind speed, strong coupling, highly nonlinear subsystems, and mass grid connections. Chaotic oscillation is one of the most typical complex dynamic behaviors of wind power systems. This behavior can seriously influence the stable operation of wind power systems and cause great harm. This study proposed a control method for finite-time function projective synchronization on the basis of the chaos synchronization principle and finite-time theory for wind power systems. Wind power systems with or without uncertain parameters were considered. First, we built a high-dimensional wind power system and analyzed its chaotic behaviors. Lyapunov exponents were derived to prove the existence of chaos and bifurcation. Second, we aimed to increase the robustness of the controller by adding parameter observers to the controller. The result helped solve the problem of unknown parameters. If a wind power system comprises unknown parameters, the unknown parameters can be defined as the system's states. An unknown parameter observer was designed to realize the identification of unknown parameters. Third, we proposed a control method for finite-time function projective synchronization. Finite-time stability theory and function projective synchronization theory were used to construct the controller. These theories can ensure the quick synchronization of a chaotic wind power system with a stable wind power system in finite time. Finally, the mathematical proof of the stability theorem was derived, and a corresponding numerical simulation was performed to validate the chaos control method for wind power systems.

Projective Synchronization of Piecewise Nonlinear Chaotic Maps

With wide applications in secure data transmission and encryption, synchronization of chaotic systems is an interesting concept and has accordingly received special attention among nonlinear systems. Here, we propose an appropriate controller for synchronizing one-parameter families of piecewise nonlinear chaotic maps using a projective synchronization method. First, we present synchronization in coupled chaos discrete-time systems using the master–slave method. Using the principle of the stability of the Lyapunov function, we design a proper controller for achieving projective synchronization of piecewise nonlinear systems. Finally, we demonstrate the applicability of the proposed scheme with simulation results.

Identical and Non-identical Synchronization of Three Scroll Unified Chaotic System (TSUCS) with Unknown Parameter Using a Modified Function Projective Control Method

This paper investigates the synchronization problem of the three-scroll unified chaotic system (TSUCS) using a modified function projective synchronization (MFPS) method. It is assumed that the parameters of both the drive and response unified chaotic systems are uncertain, while all state variables are available. First, identical synchronization of the TSUCS system is discussed with MFPS method. Then, the MFPS synchronization of TSUCS and Lu, as the two non-identical unified chaotic systems is studied. Parameter estimation strategies and feedback controllers for synchronization of the drive-response systems are designed based on the Lyapunov stability theorem and the MFPS method. The proposed synchronization scheme can be effectively utilized for synchronization of other unified chaotic systems.

On adaptive modified projective synchronization of a supply chain management system

In this paper, the synchronization problem of a chaotic supply chain management system is studied. A novel adaptive modified projective synchronization method is introduced to control the behaviour of the leader supply chain system by a follower chaotic system and to adjust the leader system parameters until the measurable errors of the system parameters converge to zero. The stability evaluation and convergence analysis are carried out by the Lyapanov stability theorem. The proposed synchronization and antisynchronization techniques are studied for identical supply chain chaotic systems. Finally, some numerical simulations are presented to verify the effectiveness of the theoretical discussions.

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.

Hybrid adaptive function projective synchronization of a hyper Lüchaotic system

In this paper, a hybrid adaptive function projective synchronization of a hyper Lu chaotic system is investigated. Firstly, according to the Lyapunov stability theory and Pecora-Carroll synchronization criterion, the controller and adaptive rate of these two kinds of synchronization methods are analyzed and designed. Then a new hybrid adaptive projective synchronization method is proposed. Finally, in order to prove the effectiveness of the proposed scheme, the comparison between those controllers is studied by simulation example.

On the dynamics, existence of chaos, control and synchronization of a novel complex chaotic system

In this paper, the authors have studied the dynamics of a novel complex chaotic system with fractional order derivative and found the existence of chaos. The novel complex system is simulated for integer as well as fractional orders which shows some unusual phenomena. The main contribution of this effort is an implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on the fractional Routh–Hurwitz stability conditions and feedback control are given. Also synchronization between a fractional order novel chaotic system and a controlled fractional order novel system using the modified adaptive projective synchronization method for different scaling matrices has been obtained. Numerical simulation results are carried out using the Adams–Bashforth–Moulton method.

Existence of Chaos, dynamical behaviour with fractional order derivatives and modified adaptive function projective synchronization with uncertain parameters of a chaotic system

In this article, the authors have studied dynamics of Duffing–Van der Pol system with fractional order derivative and found the existence of chaos. The main contribution of this effort is implementation of the Largest Lyapunov Exponent (LLE) criteria based on Wolf’s algorithm. The conditions for chaos control based on fractional Routh-Hurwitz stability conditions and feedback control are obtained. Also synchronization between fractional order chaotic system and controlled fractional order Duffing–Van der Pol system using modified adaptive function projective synchronization method for different scaling matrix has been obtained. Numerical simulation results which are carried out using Adams–Bashforth–Moulton method show that the method is easy to implement and reliable for synchronizing the two nonlinear fractional order systems.

LMI Conditions for Global Stability of Fractional-Order Neural Networks.

Fractional-order neural networks play a vital role in modeling the information processing of neuronal interactions. It is still an open and necessary topic for fractional-order neural networks to investigate their global stability. This paper proposes some simplified linear matrix inequality (LMI) stability conditions for fractional-order linear and nonlinear systems. Then, the global stability analysis of fractional-order neural networks employs the results from the obtained LMI conditions. In the LMI form, the obtained results include the existence and uniqueness of equilibrium point and its global stability, which simplify and extend some previous work on the stability analysis of the fractional-order neural networks. Moreover, a generalized projective synchronization method between such neural systems is given, along with its corresponding LMI condition. Finally, two numerical examples are provided to illustrate the effectiveness of the established LMI conditions.

Hybrid time-varying delay projective synchronization in complex dynamical networks

In this paper, a hybrid time-varying delay projective synchronization method for a complex dynamical network is proposed using a hybrid feedback controller. The existing synchronous errors of the delay projective synchronization are constant. However, the synchronous errors of the time-varying delay projective synchronization show time-varying delay. The time-varying delay projective synchronization improves the delay projective synchronization and the different component variables of the system of the node achieve a different time-varying delay projective synchronization. This paper researches the hybrid time-varying delay projective synchronization of two different types of complex dynamical network. Numerical simulations are given to demonstrate the effectiveness of the proposed synchronization scheme.

A general control method for inverse hybrid function projective synchronization of a class of chaotic systems

A general control method for inverse hybrid function projective synchronization of a class of chaotic systems

Fast projective synchronization of fractional order chaotic and reverse chaotic systems with its application to an affine cipher using date of birth (DOB)

In this paper, a fractional order dynamical system is constructed that exhibits chaotic and reverse chaotic attractors by changing the sign of the one parameter which involves in the existence of the phase reversal function. A new method of fast projective synchronization of fractional order dynamical systems is introduced. An affine cipher is proposed for secure communication based on the solutions of the synchronized fractional order chaotic systems with the support of the sender’s and receiver’s date of birth. The efficiency and security of an affine cipher are analyzed. Numerical simulations are demonstrated to show the feasibility of the presented theory.

Adaptive hybrid complex projective synchronization of chaotic complex system

In this paper defines an adaptive hybrid complex projective synchronization method to synchronize two chaotic complex systems. Base on Lyapunov stability theory, the adaptive control law and parameter update law are derived to make the state of two chaotic complex systems, which are adaptive hybrid complex projective synchronized. This paper extends projective synchronization from the field of real numbers to the field of complex numbers for a chaotic complex system. Different components of the complex system synchronized to different scale complex numbers. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive controllers.

Chaos Synchronization of the Modified Sprott E System

In this paper, chaos synchronization of the modified Sprott E system is investigated. Firstly, the chaotic attractors on different phase planes of the system are got by means of numerical simulation. When , the abundance dynamical behavior of the system is presented by the global bifurcation graph. Then, the chaos synchronization of the system by the full state hybrid projective synchronization (FSHPS) method is realized.

Projective synchronization between different fractional-order hyperchaotic systems with uncertain parameters using proposed modified adaptive projective synchronization technique

In the present article, the authors have proposed a modified projective adaptive synchronization technique for fractional-order chaotic systems. The adaptive projective synchronization controller and identification parameters law are developed on the basis of Lyapunov direct stability theory. The proposed method is successfully applied for the projective synchronization between fractional-order hyperchaotic Lu system as drive system and fractional-order hyperchaotic Lorenz chaotic system as response system. A comparison between the effects on synchronization time due to the presence of fractional-order time derivatives for modified projective synchronization method and proposed modified adaptive projective synchronization technique is the key feature of the present article. Numerical simulation results, which are carried out using Adams–Boshforth–Moulton method show that the proposed technique is effective, convenient and also faster for projective synchronization of fractional-order nonlinear dynamical systems. Copyright © 2013 John Wiley & Sons, Ltd.

A New Method for Full State Hybrid Projective Synchronization of Different Fractional Order Chaotic Systems

In this paper, the full state hybrid projective synchronization (FSHPS) between two different fractional order chaotic systems is investigated. i.e., the fractional order Chen system and the fractional order Lorenz system. Based on the synchronization error system feedback linearization theory, a new method combining feedback control is proposed for theFSHPSin fractional order chaotic systems. Numerical simulations are presented to verify the effectiveness and the feasibility of the synchronization scheme.

HIGH PRECISION FAST PROJECTIVE SYNCHRONIZATION FOR CHAOTIC SYSTEMS WITH UNKNOWN PARAMETERS

A high precision fast projective synchronization method for chaotic systems with unknown parameters was proposed by introducing optimal matrix. Numerical simulations indicate that the precision be improved about three orders compared with other common methods under the same condition of software and hardware. Moreover, when average error is less than 10-3, the synchronization speed is 6500 times than common methods, the iteration needs only 4 times. The unknown parameters also were identified rapidly. The theoretical analysis and proof also were given.

Adaptive Fuzzy Observer-based Projective Synchronization Method for Uncertain Chaotic Systems

This paper aims to develop the adaptive fuzzy observer-based projective synchronization techniques for a class of uncertain chaotic systems. An adaptive fuzzy observer is introduced to estimate the unknown system state variables. And a projective synchronization between the master and the slave systems is obtained via an adequate fuzzy adaptive controller. The dynamics of the original projective synchronization error are Strictly Positive Real (SPR). The Genesio chaotic system is employed in the simulation studies, and the results show the effectiveness of the proposed methods.

Synchronization of a New Four Dimensional Chaos System with Unknown Parameters

This paper introduces a new four-dimensional chaos system which is generated by modifying Lorenz chaos system. Some basic dynamical properties are studied. Based on projective synchronization method, dislocated projective synchronization method is presented to achieve synchronization of the new four dimensional chaos system. Numerical simulations are given to show the effectiveness of this method.

Modified projective synchronization of unknown chaotic dissipative gyroscope systems via Gaussian radial basis adaptive variable structure control

This paper proposes the modified projective synchronization method for unknown chaotic dissipative gyroscope systems via Gaussian radial basis adaptive variable structure control. Because of the nonlinear terms of the dissipative gyroscope system, the system exhibits chaotic motions. As chaotic signals are usually broadband and noise-like, synchronized chaotic systems can be used as cipher generators for secure communication. Obviously the importance of obtaining these objectives is specified when the dynamics of the gyroscope system are unknown. In this paper, using the neural variable structure control technique, control laws are established, which guarantees the modified projective synchronization of an unknown chaotic dissipative gyroscope system. Switching surfaces are adopted to ensure the stability of the error dynamics in variable structure control. In the neural variable structure control, Gaussian radial basis functions are utilized online to estimate the system dynamic functions. Also, the adaptation laws of the online estimators are derived in the sense of Lyapunov function. Thus, the unknown chaotic gyroscope system can be guaranteed to be asymptotically stable. Also, the synchronization objectives have been achieved. The proposed method allows us to arbitrarily adjust the desired scaling by controlling the slave system. It is not necessary to calculate the Lyapunov exponents and the eigenvalues of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for modified projective synchronization of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. The designed control system is robust versus model uncertainty. Numerical simulations are presented to verify the proposed synchronization method.