Adaptive Projective Synchronization Research Articles

Adaptive Hybrid Function Projective Synchronization of Chaotic Systems with Time‐Varying Parameters

The adaptive hybrid function projective synchronization (AHFPS) of different chaotic systems with unknown time‐varying parameters is investigated. Based on the Lyapunov stability theory and adaptive bounding technique, the robust adaptive control law and the parameters update law are derived to make the states of two different chaotic systems asymptotically synchronized. In the control strategy, the parameters need not be known throughly if the time‐varying parameters are bounded by the product of a known function of t and an unknown constant. In order to avoid the switching in the control signal, a modified robust adaptive synchronization approach with the leakage‐like adaptation law is also proposed to guarantee the ultimately uni‐formly boundedness (UUB) of synchronization errors. The schemes are successfully applied to the hybrid function projective synchronization between the Chen system and the Lorenz system and between hyperchaotic Chen system and generalized Lorenz system. Moreover, numerical simulation results are presented to verify the effectiveness of the proposed scheme.

Adaptive Projective Synchronization between Two Different Fractional‐Order Chaotic Systems with Fully Unknown Parameters

Projective synchronization between two different fractional‐order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional‐order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional‐order chaotic Chen system and the fractional‐order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

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 Full State Hybrid Function Projective Lag Synchronization in Chaotic Continuous-Time System

Based on the Lyapunov stability theory, an adaptive full state hybrid function projective lag synchronization (FSHFPLS) scheme is investigated in chaotic continuous-time system, and a unified adaptive controller and parameters update law are designed for achieved the projective lag synchronization up to a desired scaling function. In addition, a scheme for secure communication is presented. Numerical simulations are performed to verify and illustrate the analytical results.

Fuzzy adaptive observer-based projective synchronization for nonlinear systems with input nonlinearity

In this paper, a projective synchronization problem of master-slave chaotic systems is investigated. More specifically, a fuzzy adaptive slave chaotic system subject to both sector nonlinearities and dead-zone in the input channel is proposed using only the measurable output of the master system thanks to a suitable observer. The asymptotical projective synchronization between the master and slave systems is achieved by an adequate fuzzy adaptive variable-structure control system. The underlying parameter adaptation design as well as the asymptotical synchronization and stability analysis are carried out using a Lyapunov based approach. The distinctive feature of the control design is that the uncertainties function and the gain reduction tolerances of the dead-zone are no longer required to be known thanks to the parameter adaptation capability of the control system. The proposed synchronization scheme is extended to two classes of the master-slave chaotic systems with time-delays. By using the Lyapunov-Krasovskii approach, some stability conditions relating to these classes are derived. Simulation results are given to show the effectiveness of the proposed projective synchronization scheme.

Adaptive projective synchronization of dynamical networks with distributed time delays

In this paper, the adaptive projective synchronization of dynamical network with distributed time delays is investigated. Network with unknown topology and network with both unknown topology and system parameters of node dynamics are considered respectively. Based on Lyapunov stability theory and LaSalle’s invariance principle, the sufficient conditions for achieving projective synchronization are obtained. Numerical examples are provided to show the effectiveness of the proposed method.

A Novel Hybrid Function Projective Synchronization between Different Fractional‐Order Chaotic Systems

An adaptive hybrid function projective synchronization (AHFPS) scheme between different fractional‐order chaotic systems with uncertain system parameter is addressed in this paper. In this proposed scheme, the drive and response system could be synchronized up to a vector function factor. This proposed scheme is different with the function projective synchronization (FPS) scheme, in which the drive and response system could be synchronized up to a scaling function factor. The adaptive controller and the parameter update law are gained. Two examples are presented to demonstrate the effectiveness of the proposed scheme.

Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design

In this paper, the adaptive backstepping design is proposed for the full state hybrid projective synchronization between two different chaotic systems with fully unknown parameters. Based on the design, the synchronization of two uncertain chaotic systems is realized only by using one controller, and the unknown parameters are identified through the corresponding parameter update laws. The uncertain Genesio–Tesi chaotic system and Lorenz system are chosen as examples for detailed description of the method. Finally, some numerical simulations are given to illustrate the effectiveness of the proposed method.

Adaptive Function Projective Synchronization of Discrete Chaotic Systems with Unknown Parameters

Adaptive function projective synchronization of discrete-time chaotic systems with unknown parameters is considered. Based on the contraction mapping theorem, proper controllers and estimators are designed. Illustrative examples are provided to show the effectiveness of this method.

Adaptive Functional Projective Lag Synchronization of a Hyperchaotic Rössler System

We explain the functional projective lag synchronization of a hyperchaotic Rössler system with four unknown parameters, where the output of the master system lags behind the output of the slave system proportionally. Based on Lyapunov stability theory, an active control method and adaptive control law are employed to make the states of two hyperchaotic Rössler systems asymptotically synchronized. Finally, some numerical examples are provided to show the effectiveness of our results.

ADAPTIVE FULL STATE HYBRID PROJECTIVE SYNCHRONIZATION IN THE UNIFIED CHAOTIC SYSTEM

This paper studies the adaptive full state hybrid projective synchronization method. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with known or unknown parameters asymptotically full state hybrid projective synchronized. A unified chaotic system is used as an example and numerical simulations show the effectiveness of the scheme.

Adaptive Function Projective Synchronization of Discrete-Time Chaotic Systems

By backstepping control law and the active control method, adaptive function projective synchronization of 2D and 3D discrete-time chaotic systems with uncertain parameters are investigated. To illustrate the effectiveness of the new scheme, some numerical examples are given.

Adaptive projective synchronization in complex networks with time-varying coupling delay

In this Letter, adaptive projective synchronization (PS) between two complex networks with time-varying coupling delay is investigated by the adaptive control method, and this method has been applied to identify the exact topology of a weighted general complex network. To validate the proposed method, the Lü and Qi systems as the nodes of the networks are detailed analysis, and some numerical results show the effectiveness of the present method.

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 discrete-time 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.

Adaptive projective synchronization with different scaling factors in networks

We study projective synchronization with different scaling factors (PSDF) in N coupled chaotic systems networks. By using the adaptive linear control, some sufficient criteria for the PSDF in symmetrical and asymmetrical coupled networks are separately given based on the Lyapunov function method and the left eigenvalue theory. Numerical simulations for a generalized chaotic unified system are illustrated to verify the theoretical results.

LAG PROJECTIVE STOCHASTIC PERTURBED SYNCHRONIZATION FOR CHAOTIC SYSTEMS AND ITS APPLICATION IN SECURE COMMUNICATION

In this paper, a simple and systematic adaptive feedback method for achieving lag projective stochastic perturbed synchronization of a new four-wing chaotic system with unknown parameters is presented. Moreover, a secure communication scheme based on the adaptive feedback lag projective synchronization of the new chaotic systems with stochastic perturbation and unknown parameters is presented. The simulation results show the feasibility of the proposed method.

A function cascade synchronization method with unknown parameters and applications

This paper investigates the function cascade synchronization of chaos system. Combining cascade synchronization scheme, parametric adaptive control and projective synchronization scheme, it proposes a new function cascade synchronization scheme to address a generalized-type synchronization problem of three famous chaotic systems: the Lorenz system, Liu system and Rössler system, the states of two identical chaotic systems with unknown parameters can be asymptotically synchronized by choosing different special suitable error functions. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.

Adaptive projective synchronization and parameter identification of a class of delayed chaotic neural networks

This paper deals with the adaptive projective synchronization problem of a class of delayed neural networks. Based on Lyapunov stability theory, a new control method is proposed to achieve parameter identification and projective synchronization simultaneously. Numerical simulations were conducted to verify the effectiveness of this method.

Adaptive projective synchronization of unified chaotic systems and its application to secure communication

In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invariance principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.

Adaptive feedback controller for projective synchronization

Due to the unpredictability of the scaling factor of projective synchronization in coupled partially linear systems, it is hard to know for sure the terminal state of the synchronized dynamics. In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor onto a desired value, based on the invariance principle of differential equations. Firstly, we prove the synchronizability of the proposed simple adaptive projective synchronization control method from the viewpoint of mathematics. Then, two numerical examples are presented to illustrate the applications of the derived results. Finally, we propose a communication scheme based on the adaptive projective synchronization of the Lorenz chaotic system. Numerical simulation shows its feasibility.