Outer Synchronization Research Articles

Outer synchronization between uncertain networks with adaptive scaling function and different node numbers

We investigate outer synchronization between uncertain networks with adaptive scaling function and different node numbers. In designed synchronization strategy, the drive and response networks may differ in the node numbers and the network topologies. Moreover, the adaptive scaling function can be replaced by the adaptive law. The uncertain adjustment parameter and the uncertain coupling matrix element are identified simultaneously in the process of synchronization. Finally, the numerical example is exploited to illustrate the effectiveness of the proposed synchronization criteria.

Adaptive outer synchronization and topology identification between two complex dynamical networks with time-varying delay and disturbance

AbstractIn this paper, we investigate adaptive outer synchronization for identifying unknown network topology and parameters between two coupled complex networks with time-varying delays existing in the node dynamics and coupling forms. By designing adaptive controllers and updating laws, we obtain two theorems on the appearance of outer synchronization using Lyapunov stability theory. In the numerical examples, we provide the detailed identification criteria of network topology and system parameter according to the obtained theorems and give some numerical examples to show the efficiency of the proposed controllers.

Fixed-Time Outer Synchronization of Complex Networks with Noise Coupling**Supported by the National Natural Science Foundation of China under Grant Nos. 11711530203 and 11771443, and the Fundamental Research Funds for the Central Universities under Grant No. 2015XKMS076

In this paper, the fixed-time outer synchronization of complex networks with noise coupling is investigated. Based on the theory of fixed-time stability and matrix inequalities, sufficient conditions for fixed-time outer synchronization are established and the estimation of the upper bound of the setting time is obtained. The result shows that the setting time can be adjusted to a desired value regardless of the initial states. Numerical simulations are performed to verify the effectiveness of the theoretical results. The effects of control parameters and the density of controlled nodes on the converging time are studied.

Parameter Identification and Adaptive Control of Uncertain Goodwin Oscillator Networks with Disturbances

This paper investigates the dynamic properties of a differential equation model of mammals’ circadian rhythms, including parameter identification, adaptive control, and outer synchronization. The circadian oscillator network is described by a Goodwin oscillator network, the couplings of which are from vasoactive intestinal polypeptides described by modified Van der Pol oscillators. We build up a drive‐response system consisting of two networks with unknown parameters and disturbances. Then, we propose effective parameter updating laws to identify the unknown parameters and design adaptive control strategies to achieve outer synchronization in the drive‐response system. As special cases, two succinct corollaries are presented for different instances. All the theoretical results are proved through strict mathematical deduction based on Lyapunov stability theory, and a numerical example is also carried out to illustrate the effectiveness.

Adaptive finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation

Adaptive finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation

Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays

In this paper, we focus on the robust outer synchronization problem between two nonlinear complex networks with parametric disturbances and mixed time-varying delays. Firstly, a general complex network model is proposed. Besides the nonlinear couplings, the network model in this paper can possess parametric disturbances, internal time-varying delay, discrete time-varying delay and distributed time-varying delay. Then, according to the robust control strategy, linear matrix inequality and Lyapunov stability theory, several outer synchronization protocols are strictly derived. Simple linear matrix controllers are designed to driver the response network synchronize to the drive network. Additionally, our results can be applied on the complex networks without parametric disturbances. Finally, by utilizing the delayed Lorenz chaotic system as the dynamics of all nodes, simulation examples are given to demonstrate the effectiveness of our theoretical results.

Outer synchronization of delayed coupled systems on networks without strong connectedness: A hierarchical method

We consider the outer synchronization between drive-response systems on networks with time-varying delays, where we focus on the case when the underlying networks are not strongly connected. A hierarchical method is proposed to characterize large-scale networks without strong connectedness. The hierarchical algorithm can be implemented by some programs to overcome the difficulty resulting from the scale of networks. This method allows us to obtain two different kinds of sufficient outer synchronization criteria without the assumption of being strongly connected, by combining the theory of asymptotically autonomous systems with Lyapunov method and Kirchhoff's Matrix Tree Theorem in graph theory. The theory improves some existing results obtained by graph theory. As illustrations, the theoretic results are applied to delayed coupled oscillators and a numerical example is also given.

Research on outer synchronization between uncertain time-varying networks with different node number

We research outer synchronization between uncertain time-varying networks with different node number. Based on the Lyapunov theorem, some new sufficient synchronization criteria are proposed. Further, we design the adaptive laws of the time-varying coupling matrix element and the adjustment parameter. And the designed controller can ensure that outer synchronization between uncertain time-varying networks with different node number can be achieved perfectly. At last, numerical examples are illustrated to demonstrate the efficiency of the proposed scheme.

Analyzing synchronization of time-delayed complex dynamical networks with periodic on-off coupling

We investigate the synchronization of time-delayed complex dynamical networks with periodic on-off coupling. We derive sufficient conditions for the complete and generalized outer synchronization. Both our analytical and numerical results show that two time-delayed networks can achieve outer synchronization even if the couplings between the two networks switch off periodically. This synchronization behavior is largely dependent of the coupling strength, the on-off period, the on-off rate and the time delay. In particular, we find that the synchronization time nonmonotonically increases as the time delay increases when the time delay step is not equal to an integer multiple of the on-off period.

Coupling Effects on Synchronizability of Two-Layer Network's Projective Outer Synchronization

Based on nonlinear dynamics theory and knowledge of complex network, this paper expanded the range of two-layer network synchronization to projective outers synchronization. A mathematical model was constructed and feasibility of synchronization was demonstrated. Then we improved the model in order to study the function of different couplings [1]. Numerical examples are examined to compare the synchronizability of projective outer synchronization with different couplings. A rule called "outer small-world effect" was found due to simulation experiment. Finally, some instances were used to explain experimental results.

Adaptive finite-time outer synchronization between two complex dynamical networks with noise perturbation

In this paper, the finite-time outer synchronization between two complex dynamical networks with noise perturbation is considered. Combing the adaptive and finite-time control technologies, a novel adaptive finite-time controller is designed. Based on the finite-time stability theory of stochastic differential equations, sufficient conditions for the finite-time stochastic outer synchronization between two complex networks with identical as well as nonidentical configurations are obtained, respectively. Finally, numerical examples are examined to illustrate the effectiveness and feasibility of the theoretical results.

Outer synchronization of complex networks with internal delay and coupling delay via aperiodically intermittent pinning control

This paper concerns the outer synchronization problem between two complex delayed networks via the method of aperiodically intermittent pinning control. Apart from previous works, internal delay and coupling delay are both involved in this model, and the designed intermittent controllers can be aperiodic. The main work in this paper can be summarized as follows: First, two cases of aperiodically intermittent control with constant gain and adaptive gain are implemented, respectively. The intermittent control and pinning control are combined to reduce consumptions further. Then, based on the Lyapunov stability theory, synchronization protocols are given by strict derivation. Especially, the designed controllers are indeed simple and valid in application of theory to practice. Finally, numerical examples put the proposed control methods to the test.

Generalized outer synchronization between non-dissipatively coupled complex networks with different-dimensional nodes

• Asymptotic and exponential generalized outer synchronization criteria are proposed. • Only partial dynamics of each node in the response network is constrained by QUAD. • Our network nodes may be non-dissipatively coupled and have different dimensions. • Our network models possess different time-varying coupling configurations. • Our networks have nonlinear inner functions and different time-varying delays. This paper investigates the generalized outer synchronization (GOS) between two non-dissipatively coupled complex dynamical networks (CDNs) with different time-varying coupling delays. Our drive-response networks also possess nonlinear inner coupling functions and time-varying outer coupling configuration matrices. Besides, in our network models, the nodes in the same network are nonidentical and the nodes in different networks have different state dimensions. Asymptotic generalized outer synchronization (AGOS) and exponential generalized outer synchronization (EGOS) are defined for our CDNs. Our main objective in this paper is to design AGOS and EGOS controllers for our drive-response networks via the open-plus-closed-loop control technique. Distinguished from most existing literatures, it is the partial intrinsic dynamics of each node in response network that is restricted by the QUAD condition, which is easy to be satisfied. Representative simulation examples are given to verify the effectiveness and feasibility of our GOS theoretical results in this paper.

Outer synchronization of small-world networks by a second-order sliding mode controller

In this paper, we investigate outer synchronization of two small-world dynamical networks via second-order sliding mode control strategy. In particular, based on the coupling feature of the nodes, a message feedback chain is established. And then, the synchronization will be analyzed via pinning some nodes. By means of the second-order sliding mode theory, we propose the effective controller to realize outer synchronization between two small-world networks with a lower cost. Finally, we present some simulations to illustrate the theoretical results.

Outer synchronization and parameter identification approach to the resilient recovery of supply network with uncertainty

The resilient recovery is of great necessity and importance to supply network with uncertainty. Outer synchronization helps the supply network restores the scheduled status. Also it has absorptive and adaptive capacity. This paper proposes a resilient recovery method based on outer synchronization. Different from previous schemes, a research on supply networks with time delay, unknown parameters and structural variation has been conducted. A dynamic model of the supply network is established, in which each node is represented as a Lorenz system. Based on the Lyapunov stability theory, an impulsive pinning controller is designed for resilient recovery. Numerical simulations and related case study are used to verify the validity of the proposed model and the resilient recovery method. Experimental results show that, the proposed method can realize the parameter identification and effective recovery with various uncertain environments.

Cluster linear generalized outer synchronization in community networks via pinning control with two different switch periods

This study investigates the problem of cluster generalized outer synchronization in community networks via pinning control with two different switch periods. Several pinning controllers have been designed to achieve linear generalized outer synchronization. Using Lyapunov stability theory, sufficient linear generalized outer synchronization criteria for community networks are derived. Finally, numerical examples are presented to demonstrate the effectiveness of the theoretical results.

Generalized matrix projective outer synchronization of non-dissipatively coupled time-varying complex dynamical networks with nonlinear coupling functions

This paper investigates the generalized matrix projective outer synchronization (GMPOS) between two non-dissipatively coupled time-varying complex dynamical networks via open-plus- closed-loop dynamical compensation controllers. To be more consistent with the real-world networks, besides non-dissipatively couplings, the drive and response networks in our paper can possess different nodes, different time-varying outer coupling configuration matrices and different nonlinear inner coupling functions. Thus, our network models are more general and extensive than almost all of those in the existing literatures about outer synchronization of networks. In order to make our drive and response networks realize the GMPOS, the open-plus-closed-loop dynamical compensation controllers are designed based on the Lyapunov stability theory and Barbalat's lemma. Moreover, the speed of achieving the GMPOS between two networks can be improved by adjusting the parameters in our dynamical compensation systems. A simulation example with different hyperchaotic nodes is given to verify the effectiveness and feasibility of our theoretical results.

Finite-time outer synchronization between two complex dynamical network with time delay and noise perturbation

In this paper, the finite-time stochastic outer synchronization and generalized outer synchronization between two complex dynamic networks with time delay and noise perturbation are studied. Based on the finite-time stability theory, sufficient conditions for the finite-time outer synchronization are obtained. Numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of time delay and noise perturbation on the convergence time are also numerically demonstrated.

Adaptive outer synchronization between two complex delayed dynamical networks via aperiodically intermittent pinning control

In this paper, an aperiodically adaptive intermittent control scheme combined with pinning strategy is proposed for outer synchronization between two general complex delayed dynamical networks. Through constructing a novel piecewise auxiliary function, some sufficient conditions for outer synchronization are derived based on the reduction to absurdity and piecewise analytic method. Different from the periodically intermittent pinning control, here the adaptive intermittent pinning control can be aperiodic. Additionally, an effective pinned-node selection scheme is provided to guide what kinds of nodes should be pinned first. Numerical simulations are finally given to illustrate the effectiveness of the obtained theoretical results.

Outer synchronization between two hybrid‐coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control

This article is concerned with the problem of pinning outer synchronization between two complex delayed dynamical networks via adaptive intermittent control. At first, a general model of hybrid‐coupled dynamical network with time‐varying internal delay and time‐varying coupling delay is given. Then, an aperiodically adaptive intermittent pinning‐control strategy is introduced to drive two such delayed dynamical networks to achieve outer synchronization. Some sufficient conditions to guarantee global outer‐synchronization are derived by constructing a novel piecewise Lyapunov function and utilizing stability analytical method. Moreover, a simple pinned‐node selection scheme determining what kinds of nodes should be pinned first is provided. It is noted that the adaptive pinning control type is aperiodically intermittent, where both control period and control width are non‐fixed. Finally, a numerical example is given to illustrate the validity of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 593–605, 2016