Generalized Projective Synchronization Research Articles

Robust Adaptive Generalized Projective Synchronization of Chaotic Systems with Uncertain Disturbances

The generalized projective synchronization (GPS) of chaotic systems with uncertain parameter noise and external disturbance is discussed. Based on the adaptive technique, a response system is constructed, and a novel adaptive controller is designed to guarantee the GPS between the drive‐response systems, and to eliminate the effect of external disturbance and parameters noise on GPS. The conclusion is proved theoretically, and corresponding numerical simulations are provided to verify the effectiveness of the proposed method.

Design and implementation of fuzzy sliding mode controllers for generalized projective synchronization of chaos horizontal platform systems

This paper presents robust chattering-free fuzzy sliding mode control (FSMC) as a way to achieve generalized projective synchronization (GPS) of two horizontal chaos platform vibration systems with system uncertainty and external disturbance. An appropriate sliding surface is acquired through an SMC design such that the error state trajectories of a master–slave system will reach such a sliding surface and approaches to the origin. Based on the Lyapunov stability theory, we address the design schemes of integration fuzzy sliding mode control, where the reaching law is proposed by a set of linguistic rules and the control input is chattering free. As a consequence, the system is simulated and experimented to demonstrate that the error state tends to be stabilized and the chattering problem can be thus resolved, implying that the slave horizontal platform system (HPS) is GPS with the master HPS.

Generalized Projective Synchronization for a Class of Continuous Chaotic Systems

In this paper, a generalized projective synchronization (GPS) scheme for a class of continuous chaotic systems is investigated by using only one sate variable and its time derivatives. The construction method of response system is proposed. The mathematical proof of the GPS scheme is provided. The synchronization technique is simple and theoretically rigorous. Finally, the corresponding numerical simulation results demonstrate the effectiveness of the proposed schemes.

Two Hyperchaotic Systems with Four-wing Attractors and Their Synchronization

In this paper, an approach to generate multi-wing attractors in coupled chaotic systems is investigated. By coupling two identical Lu systems, novel four-wing hyperchaotic attractors are generated. In particular, novel four-wing hyperchaotic attractors are also generated by coupling a lorenz system and a Lu system. The paper shows that the equilibria of the proposed systems have certain symmetries with respect to specific coordinate planes. In addition, general hybrid projective dislocated synchronization between the two proposed systems is discussed, and this synchronization is applied to secure communication through chaotic masking, using the chaotic signal to mask a continuous signal and a discrete signal. In consideration of interfering random white noise, analyzes the characteristics of noise and then presents a de-noising method using wavelet transform. Simulation results show that the two systems can realize synchronization, further more, the information signal can be recovered undistorted when applying this method to secure communication.

Generalized projective synchronization of uncertain chaotic systems with external disturbance

This paper proposes the generalized projective synchronization (GPS) of uncertain chaotic systems with external disturbance via Gaussian radial basis adaptive sliding mode control (GRBASMC). A sliding surface is adopted to ensure the stability of the error dynamics in sliding mode control. In the neural sliding mode controller, a Gaussian radial basis function is utilized to online estimate the system dynamic function. The adaptation law of the control system is derived in the sense of Lyapunov function, thus the system can be guaranteed to be asymptotically stable.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 eigen values of the Jacobian matrix, which makes it simple and convenient. Also, it is a systematic procedure for GPS of chaotic systems and it can be applied to a variety of chaotic systems no matter whether it contains external excitation or not. Note that it needs only one controller to realize GPS no matter how much dimensions the chaotic system contains and the controller is easy to be implemented.The proposed method is applied to three chaotic systems: Genesio system, Lur’e like system and Duffing system.

Generalized projective synchronization between two different general complex dynamical networks with delayed coupling

In this Letter, generalized projective synchronization (GPS) between two different complex dynamical networks with delayed coupling is investigated. Two complex networks are distinct if they have diverse node dynamics, or different number of nodes, or different topological structures. By using the adaptive control scheme, a sufficient synchronization criterion for this GPS is derived based on the LaSalle invariance principle. Three corollaries are also obtained. It is noticed that the synchronization speed sensitively depends on the adjustable positive constants μ i . Furthermore, the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. In addition, the node dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition. Numerical simulations further demonstrate the feasibility and effectiveness of the theoretical results.

A new scheme of general hybrid projective complete dislocated synchronization

Based on the Lyapunov stability theorem, a new type of chaos synchronization, general hybrid projective complete dislocated synchronization (GHPCDS), is proposed under the framework of drive-response systems. The difference between the GHPCDS and complete synchronization is that every state variable of drive system does not equal the corresponding state variable, but equal other ones of response system while evolving in time. The GHPCDS includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. As examples, the Lorenz chaotic system, Rössler chaotic system, hyperchaotic Chen system and hyperchaotic Lü system are discussed. Numerical simulations are given to show the effectiveness of these methods.

GENERALIZED PROJECTIVE SYNCHRONIZATION AND PARAMETERS ESTIMATION OF TWO NEW HYPERCHAOTIC SYSTEMS WITH FULLY UNCERTAIN PARAMETERS

This paper investigates adaptive generalized projective synchronization (GPS) between two novel hyperchaotic systems with different structure and fully uncertain parameters. Based on the Lyapunov stability theorem and the adaptive control theory, GPS between the two hyperchaotic systems is achieved by proposing a new adaptive controller and a novel parameters estimation update law. Strict theoretical proof is put forward. Numerical simulations are presented to demonstrate the effectiveness of the proposed GPS scheme and verify the theoretical results.

Generalized projective synchronization of chaotic systems via adaptive learning control

In this paper, a learning control approach is applied to the generalized projective synchronisation (GPS) of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov–Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.

Hybrid dislocated control and general hybrid projective dislocated synchronization for the modified Lü chaotic system

This paper introduces a modified Lü chaotic system, and some basic dynamical properties are studied. Based on these properties, we present hybrid dislocated control method for stabilizing chaos to unstable equilibrium and limit cycle. In addition, based on the Lyapunov stability theorem, general hybrid projective dislocated synchronization (GHPDS) is proposed, which includes complete dislocated synchronization, dislocated anti-synchronization and projective dislocated synchronization as its special item. The drive and response systems discussed in this paper can be strictly different dynamical systems (including different dimensional systems). As examples, the modified Lü chaotic system, Chen chaotic system and hyperchaotic Chen system are discussed. Numerical simulations are given to show the effectiveness of these methods.

Generalized Projective Synchronization between Two Complex Networks with Time-Varying Coupling Delay

Generalized projective synchronization (GPS) between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws are designed. Feasibility of the proposed scheme is proven in theory. Moreover, two numerical examples are presented, using the energy resource system and Lü's system [Physica A 382 (2007) 672] as the nodes of the networks. GPS between two energy resource complex networks with time-varying coupling delay is achieved. This study can widen the application range of the generalized synchronization methods and will be instructive for the demand–supply of energy resource in some regions of China.

Linear generalized synchronization of chaotic systems with uncertain parameters

A more general form of projective synchronization, so called linear generalized synchronization (LGS) is proposed, which includes the generalized projective synchronization (GPS) and the hybrid projective synchronization (HPS) as its special cases. Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperchaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.

Controlling general projective synchronization of fractional order Rossler systems

This paper proposed a method to achieve general projective synchronization of two fractional order Rossler systems. First, we construct the fractional order Rossler system’s corresponding approximation integer order system. Then, a control method based on a partially linear decomposition and negative feedback of state errors was utilized on the integer order system. Numerical simulations show the effectiveness of the proposed method.