结点含时滞的具有零和非零时滞耦合的复杂网络混沌同步

时滞耦合的复杂网络同步已经有大量的研究成果,而网络结点含时滞的无时滞耦合的复杂网络同步的研究工作较少.为使网络模型更接近现实和适用更广的范围,建立了网络结点含时滞,而耦合兼零时滞(无时滞)和非零时滞(有时滞)的复杂网络同步模型.在网络结点上分别设置线性控制器和自适应控制器,研究了其混沌同步问题.利用李雅普诺夫稳定性定理,设计相应的正定函数,分别给出了复杂网络同步的充分条件.最后,为证实同步方案的有效性,选择时滞Logistic函数为结点动力系统,在兼无时滞和有时滞的网络上,给出了线性反馈控制同步误差数值演化趋势.     

复杂网络牵制控制优化选点算法及节点组重要性排序

本文研究复杂网络动力学模型的无向网络牵制控制的优化选点及节点组重要性排序问题.根据牵制控制的同步准则,网络的牵制控制同步取决于网络的Laplacian删后矩阵的最小特征值.因此,通过合理选择受控节点集得到一个较大的Laplacian删后矩阵最小特征值,是牵制控制优化选点问题的核心所在.基于Laplacian删后矩阵最小特征值的图谱性质,本文提出了多个受控节点选取的递归迭代算法,该算法适用于任意类型的网络.通过BA无标度网络、NW小世界网络及一些实际网络中的仿真实验表明:该算法在控制节点数较少时,能有效找到最优受控节点集.最后讨论了在复杂网络牵制控制背景下节点组重要性排序问题,提出节点组的重要性排序与受控节点的数目有关.     

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.     

非线性网络的动力学复杂性研究

综述了非线性网络的动力学复杂性研究在网络理论、实证和应用方面所取得的主要进展和重要成果;深刻揭示了复杂网络的若干复杂性特征与基本定量规律;提出和建立了网络科学的统一混合理论体系(三部曲)和网络金字塔,并引入一类广义Farey组织的网络家族,阐明网络的复杂性-简单性与多样性-普适性之间转变关系;揭示了网络的拓扑结构特征与网络的动态特性之间关系;建立具有长程连接的规则网络的部分同步理论并应用于随机耦合的时空非线性系统的同步;提出复杂网络的动力学同步与控制多种方法;提出若干提高同步能力的模型、方法和途径,如同步最优和同步优先模型、同步与网络特征量关系、权重作用、叶子节点影响等;提出复杂混沌网络的多目标控制及具有小世界和无标度拓扑的束流输运网络的束晕一混沌控制方法;提出集群系统的自适应同步模型及蜂拥控制方法;探讨网络上拥塞与路由控制、资源博弈及不同类型网络上传播的若干规律;揭示含权经济科学家合作网及其演化特点;实证研究并揭示了多层次的高科技企业网和若干社会网络的特点;提出一种复杂网络的非平衡统计方法,把宏观网络推进到微观量子网络.     

非线性网络的动力学复杂性研究

综述了非线性网络的动力学复杂性研究在网络理论、实证和应用方面所取得的主要进展和重要成果;深刻揭示了复杂网络的若干复杂性特征与基本定量规律;提出和建立了网络科学的统一混合理论体系(三部曲)和网络金字塔,并引入一类广义Farey组织的网络家族,阐明网络的复杂性-简单性与多样性-普适性之间转变关系;揭示了网络的拓扑结构特征与网络的动态特性之间关系;建立具有长程连接的规则网络的部分同步理论并应用于随机耦合的时空非线性系统的同步;提出复杂网络的动力学同步与控制多种方法;提出若干提高同步能力的模型、方法和途径,如同步最优和同步优先模型、同步与网络特征量关系、权重作用、叶子节点影响等;提出复杂混沌网络的多目标控制及具有小世界和无标度拓扑的束流输运网络的束晕-混沌控制方法;提出集群系统的自适应同步模型及蜂拥控制方法;探讨网络上拥塞与路由控制、资源博弈及不同类型网络上传播的若干规律;揭示含权经济科学家合作网及其演化特点;实证研究并揭示了多层次的高科技企业网和若干社会网络的特点;提出一种复杂网络的非平衡统计方法,把宏观网络推进到微观量子网络。     

复杂交通运输网络上的拥挤与效率问题研究

本文研究复杂交通运输网络上的拥挤与效率问题. 在无标度网络、随机网络以及小世界网络等不同拓扑结构中, 探讨了不同的能力分配方式和不同的OD (Origin-Destination) 交通需求分布对网络拥挤度和效率的影响. 随着平均交通需求的增加, 分析无标度网络、随机网络以及小世界网络从自由流状态到交通拥堵状态的变化规律. 为便于比较, 本文侧重研究网络拥挤度的倒数, 并将其定义为通畅度. 研究发现网络中的通畅度与效率之间存在线性相关关系, 并且不同网络中的线性比例系数 (或斜率)是不同的, 从而体现了不同网络具有不同的运输性能. 关键词： 复杂网络 拥挤 效率     

耦合含时滞的相互依存网络的局部自适应异质同步

针对由两个子网络构成的耦合含时滞的相互依存网络,研究其局部自适应异质同步问题.时滞同时存在于两个子网络的内部耦合项和子网络间的一对一相互依赖耦合项中,且网络的耦合关系满足非线性特性和光滑性.基于李雅普诺夫稳定性理论、线性矩阵不等式方法和自适应控制技术,通过对子网络设置合适的控制器,提出了使得相互依存网络的子网络分别同步到异质孤立系统的充分条件.针对小世界网络和无标度网络构成的相互依存网络进行数值模拟,验证了提出理论的正确性和有效性.     

两层星形网络的特征值谱及同步能力

多层网络是当今网络科学研究的一个前沿方向.本文深入研究了两层星形网络的特征值谱及其同步能力的问题.通过严格导出的两层星形网络特征值的解析表达式,分析了网络的同步能力与节点数、层间耦合强度和层内耦合强度的关系.当同步域无界时,网络的同步能力只与叶子节点之间的层间耦合强度和网络的层内耦合强度有关;当叶子节点之间的层间耦合强度比较弱时,同步能力仅依赖于叶子节点之间的层间耦合强度;而当层内耦合强度比较弱时,同步能力依赖于层内耦合强度;当同步域有界时,节点数、层间耦合强度和层内耦合强度对网络的同步能力都有影响.当叶子节点之间的层间耦合强度比较弱时,增大叶子节点之间的层间耦合强度会增强网络的同步能力,而节点数、中心节点之间的层间耦合强度和层内耦合强度的增大反而会减弱网络的同步能力;而当层内耦合强度比较弱时,增大层内耦合强度会增强网络的同步能力,而节点数、层间耦合强度的增大会减弱网络的同步能力.进一步,在层间和层内耦合强度都相同的基础上,讨论了如何改变耦合强度更有利于同步.最后,对两层BA无标度网络进行数值仿真,得到了与两层星形网络非常类似的结论.     

基于耦合强度的双层网络数据传输能力

为了降低网络拥塞,提升网络传输性能,对双层网络之间的耦合机理进行研究,层间关系依据度度相关性分成三种耦合方式:随机耦合、异配耦合、同配耦合.在基于最短路径路由策略和基于度的权重路由策略条件下,分析网络数据包的传输过程,并研究双层网络的耦合方式及其适合的路由策略对网络传输容量的影响.采用双层无标度网络进行仿真实验,分析在路由策略约束下传输容量和耦合方式之间的关系,依据双层网络之间耦合方式的特点,找出适合每一种路由策略的最佳耦合方式以提升网络的传输容量.经过仿真发现,采用最短路径路由策略时,异配耦合方式最佳;采用基于度的静态权重路由策略时,同配耦合方式最佳.路由策略在匹配的耦合方式下使得网络流量分配均匀,有利于网络传输容量的提升.本研究为实际网络设计和传输性能优化提供了理论基础.     

复杂网络上动力系统同步的研究进展Ⅱ——如何提高网络的同步能力

本文在上一篇综述的基础上,详细介绍了2005年以来复杂网络上动力系统同步研究的最新进展,特别着重于如何提高网络同步能力方面的研究.文章首先介绍了最近有关网络结构与同步能力之间细致关系的研究,然后重点介绍了提高复杂网络同步能力的两种方法:调节耦合强度和改变网络结构,文章最后回答了上一篇综述提出的几个问题,并指出了这一领域几个新的有待解决的问题和可能的发展方向.     

Pinning synchronization of time-varying polytopic directed stochastic networks

In this Letter, pinning synchronization of a directed network with Markovian jump (DNMJ) and nonlinear perturbations is considered. By analyzing the structure of the network, a detailed pinning scheme is given to ensure the synchronization of all nodes in a DNMJ. This pinning scheme can overcome those difficulties on deciding which nodes needs to be pinned. This scheme can also identify the exact least number of pinned nodes for a DNMJ model. In addition, the time-varying polytopic directed network with Markovian jump is discussed. Finally, examples are provided to illustrate the effectiveness of the gained criteria.     

Novel pinning control strategies for synchronisation of complex networks with nonlinear coupling dynamics

This paper considers the global stability of controlling an uncertain complex network to a homogeneous trajectory of the uncoupled system by a local pinning control strategy. Several sufficient conditions are derived to guarantee the network synchronisation by investigating the relationship among pinning synchronisation, network topology, and coupling strength. Also, some fundamental and yet challenging problems in the pinning control of complex networks are discussed: (1) what nodes should be selected as pinned candidates? (2) How many nodes are needed to be pinned for a fixed coupling strength? Furthermore, an adaptive pinning control scheme is developed. In order to achieve synchronisation of an uncertain complex network, the adaptive tuning strategy of either the coupling strength or the control gain is utilised. As an illustrative example, a network with the Lorenz system as node self-dynamics is simulated to verify the efficacy of 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.     

Pinning control of scale-free dynamical networks

Recently, it has been demonstrated that many large complex networks display a scale-free feature, that is, their connectivity distributions have the power-law form. In the present work, control of a scale-free dynamical network by applying local feedback injections to a fraction of network nodes is investigated. The specifically and randomly pinning schemes are considered. The specifically pinning of the most highly connected nodes is shown to require a significantly smaller number of local controllers as compared to the randomly pinning scheme. The method is applied to an array of Chua's oscillators as an example.     

Optimal pinning synchronization on directed complex network

In this paper, pinning synchronization on directed network was considered. By analyzing, some general synchronization criteria on directed network were established. And then, we verified it on directed globally coupled network, directed scale-free network, and directed small-world network, respectively. The pinning nodes were selected, respectively, according to order of in-degrees and out-degrees. Through comparing and analyzing simulations, the optimal pinning scheme was found, and a practical principle was induced finally.     

Effects of degree correlation on the controllability of networks

In this paper, we investigate the effects of degree correlation on the controllability of undirected networks with different degree-mixing patterns based on simulation analysis. Considering random pinning, max-degree pinning and mix-degree pinning, some relevance factors on controllability such as the control gain and the number of pinned nodes are discussed in detail. It is found that disassortative mixing enhances the network controllability contrast to assortative mixing, to which the network controllability is sensible. Furthermore, too large or too low value of the feedback gain can reduce the controllability. From the viewpoint of practical application, mix-degree pinning strategy is suggested in assortative network, while in disassortative network, max-degree pinning scheme is better than random pinning.     

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.     

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.     

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.     

Disturbance rejection and H∞ pinning control of linear complex dynamical networks

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances.A dynamical network is said to be robust to disturbance,if the H ∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small.It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H ∞ control problem of a set of independent systems whose dimensions are equal to that of a single node.A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node.To improve this,local feedback injections are applied to a small fraction of the nodes in the network.Some criteria for possible performance improvement are derived in terms of linear matrix inequalities.It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.