具有双重时滞的时变耦合复杂网络的牵制外同步研究

针对同时具有节点时滞和耦合时滞的时变耦合复杂网络的外同步问题, 提出一种简单有效的自适应牵制控制方法. 首先构建一种贴近实际的驱动-响应复杂网络模型, 在模型中引入双重时滞和时变不对称外部耦合矩阵. 进一步设计易于实现的自适应牵制控制器, 对网络中的一部分关键节点进行控制. 构造适当的Lyapunov泛函, 利用 LaSalle不变集原理和线性矩阵不等式, 给出两个复杂网络实现外同步的充分条件. 最后, 仿真结果表明所提同步方法的有效性, 同时揭示耦合时滞对同步收敛速度的影响.     

Generalized projective synchronization of fractional-order complex networks with nonidentical nodes

<正>This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 < q < 1 is obtained based on the stability theory of the fractional-order system.The control method which combines active control with pinning control is then suggested to obtain the controllers.Furthermore,the adaptive strategy is applied to tune the control gains and coupling strength.Corresponding numerical simulations are performed to verify and illustrate the theoretical results.     

Adaptive synchronization of weighted complex dynamical networks through pinning

This paper considers the problem of controlling weighted complex dynamical networks by applying adaptive control to a fraction of network nodes. We investigate the local and global synchronization of the controlled dynamical network through the construction of a master stability function and a Lyapunov function. Analytical results show that a certain number of nodes can be controlled by using adaptive pinning to ensure the synchronization of the entire network. We present numerical simulations to verify the effectiveness of the proposed scheme. In comparison with feedback pinning, the proposed pinning control scheme is robust when tested by noise, different weighting and coupling structures, and time delays.     

Synchronisation in networks of delay-coupled type-I excitable systems

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.     

Meyer–Neldel energy in Se-based binary and ternary chalcogenide glasses

This paper investigates the cluster-modified function projective synchronisation (CMFPS) of a generalised linearly coupled network with asymmetric coupling and nonidentical dynamical nodes. A novel synchronisation scheme is proposed to achieve CMFPS in community networks. We use adaptive control method to derive CMFPS criteria based on Lyapunov stability theory. Each cluster of networks is synchronised with target system by state transformation with scaling function matrix. Numerical simulation results are presented finally to illustrate the effectiveness of this method.     

Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control

The problem of synchronization for a class of complex delayed dynamical networks via pinning periodically intermittent control is considered in this Letter. Some novel and useful exponential synchronization criteria are obtained by utilizing the methods which are different from the techniques employed in the existing works, and the derived results are less conservative. Especially, the traditional assumptions on control width and time delays are released in our results. Moreover, a pinning scheme deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength is provided. A Barabási-Albert network example is finally given to illustrate the effectiveness of the theoretical results.     

Modeling and adaptive pinning synchronization control for a chaotic-motion motor in complex network

We introduce a chaos model for a permanent-magnet synchronous motor and construct a coupled chaotic motor in a complex dynamic network using the Newman–Watts small-world network algorithm. We apply adaptive pinning control theory for complex networks to obtain suitable adaptive feedback gain and the number of nodes to be pinned. Nodes of low degree are pinned to realize global asymptotic synchronization in the complex network. The proposed adaptive pinning controller is added to the complex motor network for simulation and verification.     

Cluster synchronization in community network with nonidentical nodes via intermittent pinning control

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. By combining intermittency with a pinning control scheme, some effective controllers are designed. In the control scheme, only one node in each community is controlled and coupling weights of a spanning tree in each community are enhanced. Based on the Lyapunov function method and mathematical analysis technique, two results for achieving cluster synchronization are obtained. Noticeably, by introducing an adaptive strategy, some universal adaptive intermittent pinning controllers are designed for different networks. Finally, two numerical simulations are performed to verify the correctness of the derived results.     

Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.     

基于低阶矩阵最大特征值的复杂网络牵制混沌同步

虽已对复杂网络牵制同步需要牵制结点数量及牵制结点数量与耦合强度的关系进行了研究,然而快速计算牵制结点数量仍是大规模复杂网络面临的一个重要问题.研究发现了复杂网络耦合矩阵主子阵最大值递减规律,由此提出了快速计算复杂网络牵制结点数量的方法,揭示了不同的牵制策略与牵制结点数量之间的关系.数值仿真显示了在无标度网络和小世界网络上三种不同的牵制策略下,牵制结点数与主子阵最大特征值的变化规律;最后给出了一个在无标度网络上采用随机选择结点策略的牵制同步实例.     

Generalized chaos synchronization of a weighted complex network with different nodes

This paper proposes a method of realizing generalized chaos synchronization of a weighted complex network with different nodes. Chaotic systems with diverse structures are taken as the nodes of the complex dynamical network, the nonlinear terms of the systems are taken as coupling functions, and the relations among the nodes are built through weighted connections. The structure of the coupling functions between the connected nodes is obtained based on Lyapunov stability theory. A complex network with nodes of Lorenz system, Coullet system, Rõssler system and the New system is taken as an example for simulation study and the results show that generalized chaos synchronization exists in the whole weighted complex network with different nodes when the coupling strength among the nodes is given with any weight value. The method can be used in realizing generalized chaos synchronization of a weighted complex network with different nodes. Furthermore, both the weight value of the coupling strength among the nodes and the number of the nodes have no effect on the stability of synchronization in the whole complex network.     

Pinning control of complex dynamical networks with general topology

Recently, the researches on pinning control of complex dynamical networks have mainly focused on such networks with very specific coupling schemes (e.g., symmetric coupling, uniform coupling and linear coupling). However, most real networks often consist of local units, which interact with each other via asymmetric and heterogeneous connections. In this paper, pinning control of a continuous-time complex dynamical network with general coupling topologies is studied. Some generic stability criteria based on master stability function (MSF) are derived for such a general controlled network, which guarantee that the whole network can be pinned to its equilibrium by placing feedback control only on a small fraction of nodes. Then, these results are extended to discrete-time case. Previous results about symmetric, uniform or linear coupled networks in this area are included as special cases of the present work. Numerical simulations of directed networks with weighted coupling pinned by specifically selective pinning scheme are given for illustration and verification.     

Adaptive Synchronization of Fractional Order Complex-Variable Dynamical Networks via Pinning Control

In this paper, the synchronization of fractional order complex-variable dynamical networks is studied using an adaptive pinning control strategy based on close center degree. Some effective criteria for global synchronization of fractional order complex-variable dynamical networks are derived based on the Lyapunov stability theory. From the theoretical analysis, one concludes that under appropriate conditions, the complex-variable dynamical networks can realize the global synchronization by using the proper adaptive pinning control method. Meanwhile, we succeed in solving the problem about how much coupling strength should be applied to ensure the synchronization of the fractional order complex networks. Therefore, compared with the existing results, the synchronization method in this paper is more general and convenient. This result extends the synchronization condition of the real-variable dynamical networks to the complex-valued field, which makes our research more practical. Finally, two simulation examples show that the derived theoretical results are valid and the proposed adaptive pinning method is effective.     

Cluster synchronization in the adaptive complex dynamical networks via a novel approach

This Letter investigates cluster synchronization in the adaptive complex dynamical networks with nonidentical nodes by a local control method and a novel adaptive strategy for the coupling strengths of the networks. In this approach, the coupling strength of each node adjusts adaptively only based on the state information of its neighborhood. By means of the proposed scheme, the sufficient conditions for achieving cluster synchronization are derived analytically by utilizing Lyapunov stability theory. It is demonstrated that the synchronization performance is sensitively affected by the control gain, the inner-coupling matrix and the network topological structure. The numerical simulations are performed to verify the effectiveness of the theoretical results.     

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper,the pinning synchronization problem of stochastic delayed complex network (SDCN) is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller,where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller,some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.     

Adaptive pinning synchronization in fractional-order complex dynamical networks

Synchronization of general complex dynamical networks with fractional-order dynamical nodes is addressed in this paper. Based on the stability theory of fractional-order differential systems and adaptive pinning control, some sufficient local asymptotical synchronization criteria and global asymptotical ones are derived respectively, which succeed in solving the problem about how many nodes are need to be controlled and how much coupling strength should be applied to ensure the synchronization of the entire fractional-order networks. The obtained results are more general and effective than those reported. Moreover, the coupling-configuration matrices and the inner-coupling matrices are not assumed to be symmetric and irreducible. Finally, a numerical simulation is presented to demonstrate the validity and feasibility of the proposed synchronization criteria.     

Synchronizability on complex networks via pinning control

It is proved that the maximum eigenvalue sequence of the principal submatrices of coupling matrix is decreasing. The method of calculating the number of pinning nodes is given based on this theory. The findings reveal the relationship between the decreasing speed of maximum eigenvalue sequence of the principal submatrices for coupling matrix and the synchronizability on complex networks via pinning control. We discuss the synchronizability on some networks, such as scale-free networks and small-world networks. Numerical simulations show that different pinning strategies have different pinning synchronizability on the same complex network, and the consistence between the synchronizability with pinning control and one without pinning control in various complex networks.     

Cluster synchronization in fractional-order complex dynamical networks

Cluster synchronization of complex dynamical networks with fractional-order dynamical nodes is discussed in the Letter. By using the stability theory of fractional-order differential system and linear pinning control, a sufficient condition for the stability of the synchronization behavior in complex networks with fractional order dynamics is derived. Only the nodes in one community which have direct connections to the nodes in other communities are needed to be controlled, resulting in reduced control cost. A numerical example is presented to demonstrate the validity and feasibility of the obtained result. Numerical simulations illustrate that cluster synchronization performance for fractional-order complex dynamical networks is influenced by inner-coupling matrix, control gain, coupling strength and topological structures of the networks.     

Pinning a complex dynamical network via impulsive control

Complex dynamical networks are being studied across many fields of science and engineering today. The issue of controlling a network to the desired state has attracted increasing attention. In this Letter, we investigate the problem of pinning a complex dynamical network to the solution of an uncoupled system. Our strategy is to apply impulsive control to a small fraction of network nodes. Based on the Lyapunov stability theory, we prove that the theoretical results derived here are effective. In addition, a B-A scale-free network with 20 nodes is taken for illustration and verification.     

Synchronization in uncertain complex networks

We consider the problem of synchronization in uncertain generic complex networks. For generic complex networks with unknown dynamics of nodes and unknown coupling functions including uniform and nonuniform inner couplings, some simple linear feedback controllers with updated strengths are designed using the well-known LaSalle invariance principle. The state of an uncertain generic complex network can synchronize an arbitrary assigned state of an isolated node of the network. The famous Lorenz system is stimulated as the nodes of the complex networks with different topologies. We found that the star coupled and scale-free networks with nonuniform inner couplings can be in the state of synchronization if only a fraction of nodes are controlled.