Synchronization Of Drive-response Dynamical Networks Research Articles

Robust projective lag synchronization in drive-response dynamical networks via adaptive control

This paper investigates the problem of projective lag synchronization behavior in drive-response dynamical networks (DRDNs) with identical and non-identical nodes. An adaptive control method is designed to achieve projective lag synchronization with fully unknown parameters and unknown bounded disturbances. These parameters were estimated by adaptive laws obtained by Lyapunov stability theory. Furthermore, sufficient conditions for synchronization are derived analytically using the Lyapunov stability theory and adaptive control. In addition, the unknown bounded disturbances are also overcome by the proposed control. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Simulation results show the effectiveness of the proposed method.

Projective lag synchronization in drive-response dynamical networks with delay coupling via hybrid feedback control

This paper investigates the problem of projective lag synchronization behavior with delayed coupling in drive-response dynamical network model consisting of identical and nonidentical nodes. Based on Lyapunov stability theory, a hybrid feedback control method is designed to achieve the projective lag synchronization with constant time delay and with time-varying coupling delay. In addition, the control will deal with and without mismatched terms. Finally, analytical results show that the states of the dynamical network with delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulation results demonstrate the validity of the proposed method.

Outer synchronization of drive-response dynamical networks via adaptive impulsive pinning control

In this paper, outer synchronization between drive and response networks via adaptive impulsive pinning control is investigated. In the pinning control scheme, the controlled nodes are changed adaptively according to the synchronization errors at different impulsive instants. Based on the Lyapunov function method and mathematical analysis, a synchronization criterion is precisely derived. Under this criterion, the impulsive intervals for achieving outer synchronization of two given networks are estimated. Further, an adaptive strategy is designed for a node-to-node pinning impulsive controller, with a corresponding synchronization condition derived. In the proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is developed and evaluated. The theoretical results are illustrated to be effective by several numerical examples.

Projective lag synchronization in drive-response dynamical networks

This paper investigates projective lag synchronization (PLS) behavior between chaotic systems in drive-response dynamical networks (DRDNs) model with nonidentical nodes. A hybrid feedback control method is designed to achieve the PLS with and without mismatched terms. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally, analytical results show that the states of the dynamical network with non-delayed coupling can be asymptotically synchronized onto a desired scaling factor under the designed controller. Moreover, the numerical simulations results demonstrate the validity of the proposed method.

Weak Projective Synchronization in Drive-Response Dynamical Networks with Time-Varying Delay and Parameter Mismatch

This paper investigates the problem of projective synchronization in drive-response dynamical networks (DRDNs) with time-varying delay and parameter mismatch via impulsive control. Owing to projective factor and parameter mismatch, complete projective synchronization cannot be achieved. Therefore, a weak projective synchronization scheme is proposed to ensure that the DRDNs are in a state of synchronization with an error level. Based on the stability analysis of the impulsive functional differential equations, a general method of the weak projective synchronization with the error level is derived in DRDNs. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results.

Synchronization in Drive-Response Dynamical Networks Based on Nonlinear Control

In this paper, synchronization in drive-response dynamical networks is investigated. By using the Gerschgorins disk theorem and the stability theory, a nonlinear controller is designed to make the drive-response dynamical networks synchronized. Some sufficient conditions for achieving the synchronization of the drive-response dynamical networks are derived. The structure of the network can be random, regular, small-world, or scale-free. A numerical example is given to demonstrate the validity of the proposed method, in which the famous Lorenz system is chosen as the nodes of the network. Simulation results have verified the correctness and effectiveness of the proposed scheme. Moreover, it is worth noting that the time used for achieving synchronization of the drive-response dynamical networks sensitively depends on the coupling strength .

Adaptive pinning control for the projective synchronization of drive-response dynamical networks

This paper studies the projective synchronization of a drive-response dynamical network of partially linear systems. The coupling-configuration matrix of the network is not necessarily symmetric. Two adaptive pinning control strategies are derived based on the Barbalat’s Lemma. In the first control strategy, the pinning control gain is adaptively updated to realize the projective synchronization. In the second control strategy, both the pinning control gain and the coupling strength between nodes are adaptively updated. Numerical simulation results show that the coupling strength needed in the second control strategy is smaller than that in the first control strategy to achieve the projective synchronization of the network.

Adaptive open-plus-closed-loop method of projective synchronization in drive-response dynamical networks

This paper investigates the problem of projective synchronization (PS) in drive-response dynamical networks (DRDNs) with mismatched terms. Based on the adaptive open-plus-closed-loop (AOPCL) method, a general method of PS is derived in DRDNs, which is robust to limited accuracy of data and effects of noise. Moreover, the feedback gains of the closed loop control part can be automatically adapted to suitable constants. Corresponding numerical simulations on Lorenz system are performed to verify and illustrate the analytical results.

Projective cluster synchronization in drive-response dynamical networks

In this paper, we study the projective cluster synchronization in a drive-response dynamical network with 1 + N coupled partially linear chaotic systems. Because the scaling factors characterizing the dynamics of projective synchronization remain unpredictable, pinning control ideas are adopted to direct the different scaling factors onto the desired values. It is also shown that the projection cluster synchronization can be realized by controlling only one node in each cluster. Numerical simulations on the chaotic Lorenz system are illustrated to verify the theoretical results.

Projective synchronization in drive-response dynamical networks

Projective synchronization (characterized by a scaling factor α ) and its control have recently been well investigated in two coupled chaotic oscillators, but it has not been realized yet in the case of more than two chaotic systems. In this paper, we study the projective synchronization in 1 + N coupled chaotic systems by introducing a drive-response dynamical networks model. Furthermore, pinning control techniques are also adopted to direct the scaling factor onto the desired value. It is also shown that the projection synchronization of the drive-response dynamical networks can be realized by controlling only one node. Numerical simulations on the chaotic Lorenz system are illustrated to verify the theoretical results.