Search

We research the synchronization problem of complex network composed of N Duffing circuits. Firstly, we theoretically fit the synchronization experiment between a Duffing circuit and another Duffing circuit driven by linear coupling, and get the results consistent with the experiment. Furthermore, the synchronization technology between two Duffing circuits is extended to the synchronization of complex network composed of N Duffing circuits. Based on the stability theorem, the conditions for realizing network synchronization are determined by calculating the Lyapunov exponent of each response Duffing circuit system. Finally, the correctness of the theoretical analysis is verified by simulation. • We research the synchronization problem of complex network composed of N Duffing circuits. • The synchronization technology between two Duffing circuits is extended to the network synchronization. • The results of theoretical analysis are consistent with those of experiment. [ABSTRACT FROM AUTHOR]

In this paper, a new technology is proposed to research the problem of the synchronization transmission of spiral wave and turbulence between uncertain time-delay neuronal networks with different node numbers and topologies. In order to construct the Lyapunov–Krasovskii functional of the network, a special function is designed. According to our scheme, the uncertain time-delay neuronal network can transfer synchronously the spiral wave and turbulence, especially the chattering near the synchronization target can also be eliminated, which indicates that the synchronization performance of the network is more stable. At the same time, the recognition law of the network coupled matrix element is also designed to replace effectively the uncertain coupled matrix element in the network. • Synchronization transmission of spiral wave and turbulence in uncertain time-delay neuronal networks is researched. • The networks may differ in the node numbers and the network topologies. • A special function is designed to construct the Lyapunov–Krasovskii functional of the network. • The recognition law of the network coupled matrix element is designed. [ABSTRACT FROM AUTHOR]

Abstract A new strategy is designed to research the synchronization transmission of laser pattern signals between uncertain networks constructed by Gibbs laser spatial expanded models. First, we introduce the output characteristics of the Gibbs laser spatial expanded model and show the typical spatiotemporal patterns. Furthermore, we select Gibbs laser spatial expanded models to constitute the laser networks and to realize the synchronization transmission of the laser signals between the networks. The synchronization strategy allows the existence of uncertain or unknown parameters in the network and these parameters can be replaced by the designed identification law. At the same time, the synchronization performance of the networks is not affected by the network topology and the number of nodes. Especially, the structure of the designed network controller is simple, which is very convenient for practical application. Highlights • Synchronization transmission of laser pattern signals between uncertain networks is investigated. • Synchronization strategy allows the existence of uncertain or unknown parameters in the network. • Synchronization performance of the networks is not affected by the network topology and the node numbers. • The structure of the designed network controller is simple. [ABSTRACT FROM AUTHOR]

Abstract We investigate the exponential synchronization of uncertain networks with the switching topology based on sliding mode technology. In this work, the network controller and the adaptive law of uncertain parameter are designed to ensure the exponential synchronization between uncertain networks with the switching topology and the synchronization target. In addition, the synchronization technology is suitable for any topology network, and in the network synchronization process, the switching of the network topology is not restricted, that is, it can be switched at any time according to the actual requirement. At last, the effects of the exponential synchronization criteria are verified through the numerical example. Highlights • Exponential synchronization of uncertain networks based on sliding mode technology is investigated. • The synchronization technology is suitable for any topology network. • The network controller and the adaptive law of uncertain parameter are designed. • The switching of the network topology is not restricted. [ABSTRACT FROM AUTHOR]

Abstract We investigate the cluster synchronization in uncertain network with nonidentical nodes based on adaptive pinning control. In this synchronization technology, the network can be arbitrarily divided into several clusters. And the network parameters can be uncertain and they follow a kind of the identification law. By utilizing pinning control strategy, cluster synchronization criterion for the uncertain network has been established. Finally, the numerical simulation is provided to prove the effectiveness of proposed pinning control strategy. Highlights • Cluster synchronization in uncertain network based on adaptive pinning control is researched. • The network parameters can be uncertain and they follow a kinds of the identification law. • Cluster synchronization criterion for the uncertain network has been established. • The node dynamics belonging to different clusters are diverse. [ABSTRACT FROM AUTHOR]

In this work, the synchronization between uncertain time-delayed networks with multi-link and different topologies is investigated. We design the suitable identification laws to tackle the uncertain parameters in the drive and response networks. And we also design the adaptive laws to determine the configuration matrix elements of the networks. This synchronization strategy allows the driver and response networks to have different topologies. And it is unnecessary to solve the eigenvalues of the network node equations. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract We concentrate on the synchronization problem of the uncertain time-delayed network with multi-link. In this work, we design a novel technology to obtain the network synchronization condition so that we do not need to solve the Jacobi matrices of the state equations at the network nodes. Moreover, the uncertain parameters in state equations at the network nodes can also be identified simultaneously in the process of synchronization. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach. Our results are suitable for the multi-link network with arbitrary topology. And the dynamical network with single-link can be considered as a special case of dynamical network with multi-link. Highlights • We design a novel technology to obtain the network synchronization condition. • The uncertain parameters at the network nodes can be identified. • The results are suitable for the multi-link network with arbitrary topology. • The single-link network can be considered as a special case of multi-link network. [ABSTRACT FROM AUTHOR]

We research cluster synchronization transmissions of different external signals in discrete uncertain network. Based on the Lyapunov theorem, the network controller and the identification law of uncertain adjustment parameter are designed, and they are efficiently used to achieve the cluster synchronization and the identification of uncertain adjustment parameter. In our technical scheme, the network nodes in each cluster and the transmitted external signal can be different, and they allow the presence of uncertain parameters in the network. Especially, we are free to choose the clustering topologies, the cluster number and the node number in each cluster. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We research synchronization of uncertain time-varying network based on sliding mode control technique. The sliding mode control technique is first modified so that it can be applied to network synchronization. Further, by choosing the appropriate sliding surface, the identification law of uncertain parameter, the adaptive law of the time-varying coupling matrix element and the control input of network are designed, it is sure that the uncertain time-varying network can synchronize effectively the synchronization target. At last, we perform some numerical simulations to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

We consider the synchronization transmission problem of spiral wave and turbulence within the uncertain switching network. Through constructing reasonably the Lyapunov function of the network, the uncertain switching network not only can transfer synchronously the spiral wave and turbulence originated from the synchronization target, but also the chattering near the synchronization target can be eliminated, which indicates that the synchronization performance of the network is more stable. At the same time, the adaptive laws of the uncertain parameters are designed and the uncertain parameters in the switching network nodes are replaced effectively. [ABSTRACT FROM AUTHOR]

We modify sliding mode control technique from the synchronization of a single dynamic system to the synchronization of complex network. Projective synchronization of uncertain scale-free network is investigated based on modified sliding mode control technique. Further, the sliding surfaces, the identification laws of uncertain parameters and the control inputs are designed, and the condition of realizing projective synchronization of uncertain scale-free network is obtained. Finally, the Logistic systems with chaotic behavior are taken as nodes to constitute the scale-free network and the synchronization target. The simulation results show that the synchronization mechanism is effective. [ABSTRACT FROM AUTHOR]

We propose a new technique for the cluster synchronization between uncertain networks with different dynamics. Based on the Lyapunov theorem and Lipschitz condition, the network controllers and the identification laws of uncertain parameters are designed, and they are efficiently used to achieve the cluster synchronization and the identification of uncertain parameters. Particularly in our work, the dynamics of nodes in different clusters can be different. And there are not any limitations for the division of the clusters, the number of nodes in each cluster and the connections between nodes. [ABSTRACT FROM AUTHOR]

In this paper, a new method is presented for the synchronization transmission of spatiotemporal chaotic signal in the uncertain time-varying network. By designing a special function to construct the Lyapunov function of the network, it is sure that the uncertain time-varying network can effectively synchronize the spatiotemporal chaotic signal generated by the synchronization target. At the same time, we also design the identification laws of uncertain parameters and the adaptive laws of the time-varying coupling matrix elements. Especially in our work, the nodes of the uncertain time-varying network and the synchronization target are different. Obviously, this research has the reference value for the application fields. [ABSTRACT FROM AUTHOR]

In this work, we design a novel synchronization technique to realize the synchronization of the network group which is constituted by some uncertain discrete networks with diverse structures. Based on Lyapunov theorem, the selection principle of the control inputs and identification law of uncertain parameters in networks are determined, and the synchronization conditions of network group are obtained. Finally, numerical simulations using one-dimensional convective equations with spatiotemporal chaos behaviors illustrate the performance of the synchronization scheme. The research results show that our synchronization technique can be suitable for the network connecting arbitrarily, and not only the network number but also node number in each network can also be chosen freely. [ABSTRACT FROM AUTHOR]

In this paper, we research the outer synchronization among discrete networks with different topologies. Based on Lyapunov theorem, a novel synchronization technique is designed. Further, the control inputs of the networks and the adaptive laws of configuration matrix element are obtained. In the end, a numerical example is given to illustrate the effectiveness of the synchronization technique. It is found that the designed control input of the networks ensures the convergence of the errors among the networks to zero. And the designed adaptive law of configuration matrix element can replace effectively configuration matrix element in networks. [ABSTRACT FROM AUTHOR]

We propose a novel scheme to achieve synchronization tracking of uncertain discrete network with spatiotemporal chaos behaviors. In this work, the traditional method of sliding mode control is firstly modified for researching conveniently the synchronization tracking of uncertain discrete network. Further, the network sliding mode surface and control input are designed, and their effectiveness are analyzed. At the same time, we also design the adaptive law to identify availably the uncertain configuration coefficient of the network sliding mode surface. Finally, an example about the small-world network is considered to illustrate the application and effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

We design a novel synchronization technique to research the synchronization of network group constituted of uncertain networks with different structures. Based on Lyapunov theorem, the selection principles of the control inputs and the parameter identification laws of the networks are determined, and synchronization conditions of the network group are obtained. Some numerical simulations are provided to verify the correctness and effectiveness of the synchronization technique. We find that the network number, the number of network nodes and network connections indeed will not affect the stability of synchronization of network group. [ABSTRACT FROM AUTHOR]

In this work, we research the parameter estimation and synchronization in the uncertain financial network. First, we introduce the characteristics of a typical financial system. And we design an observer to effectively estimate the uncertain parameter in the system. On this basis, we research the synchronization of the uncertain financial network consisting of several financial systems. The conditions of network synchronization are obtained by calculating the Lyapunov exponent of the network. Finally, we test the network synchronization performance using numerical simulation. This technique does not need to design the network controller or the control input, it is simple and convenient for practical application. [ABSTRACT FROM AUTHOR]

We research the synchronization transmission of the target signal in the circuit network composed of modified autonomous Van der Pol-Duffing (MAVPD) circuit based on coupling technique. First, we introduce the characteristics of MAVPD circuit. At the same time, the synchronization transmission of the target signal originated from a single MAVPD circuit is researched based on the coupling technique. By calculating the Lyapunov exponent of the coupling circuit, the range of the coupling coefficient is determined when the target signal is transmitted synchronously. Furthermore, the MAVPD circuits are used as the nodes to construct the circuit network, and the synchronization transmission of the target signal in the circuit network is researched. Finally, we test the effect of noise on network synchronization performance. • Synchronization transmission of the target signal in the circuit network is researched. • The Lyapunov exponent of the network is calculated as the synchronization criterion. • We test the effect of noise on network synchronization performance. [ABSTRACT FROM AUTHOR]

In this work, we design a coupling technology to achieve synchronization between uncertain delay networks. Based on the Lyapunov theorem, we further determine the adaptive laws of the uncertain parameter and the coupling coefficient, and the conditions for achieving network synchronization are derived analytically. Our synchronization strategy can be applied to more general complex dynamical networks. In the process of synchronization, there are not any limitations for the connections between network nodes, and the number of network node can be selected freely. A simulation example is given to verify the effectiveness and feasibility of our theoretical results. • A coupling technology is designed to achieve synchronization between uncertain delay networks. • The adaptive laws of the uncertain parameter and the coupling coefficient are determined. • Synchronization performance of the networks is not affected by the network topology and the node numbers. [ABSTRACT FROM AUTHOR]

We research the synchronization between uncertain spatiotemporal networks by using open-loop and closed-loop coupling technology. Based on the stability theorem, we construct a suitable Lyapunov function to determine the open-loop and closed-loop coupling function between networks, and obtain the conditions of network synchronization. At the same time, we design the identification law of uncertain parameters, which effectively replaces the uncertain parameters in the response network. Finally, the effectiveness of synchronization scheme is verified by the numerical simulation. The technology can achieve network synchronization without designing the network controllers, so it has stronger practicability. [ABSTRACT FROM AUTHOR]