复杂网络的同步: 理论、方法、应用与展望

复杂网络随处可见, 如互联网、电力网络、商业网络、生物神经网络、社会关系网等. 这些复杂网络与我们的生活息息相关, 对它们的深入研究不但会促进许多重要科学分支的发展而且可能引起人类社会生活方式的根本变革. 同步是自然界中广泛存在的一类非常重要的非线性现象, 复杂网络展示了丰富多彩的网络同步现象. 在过去10年里, 不同研究领域的学者从不同的角度广泛而深入地开展了复杂网络同步的研究. 本文简要的回顾国内外过去10年在复杂网络同步领域的主要研究进展, 包括理论、方法、应用与展望, 试图推进国内复杂网络同步的研究.      

基于脉冲控制下的复杂时滞动力网络的鲁棒同步

近年来复杂网络已经引起了科学和工程技术等各个领域的广泛关注,尤其是复杂网络中的非线性动力学行为,以及网络的拓扑结构如何影响它的动力学行为的研究,已成为当前一项极其重要的战略课题.本文主要讨论基于脉冲控制下复杂时滞动力网络的同步动力学,应用时滞动力系统的脉冲控制理论,给出了复杂时滞动力网络的一些简单而又一般的鲁棒同步化准则,这些准则能够提供一个新的和有效的控制方法来同步一个任意给定的时滞动力网络到一个期望的同步态,进一步地将所获得的结果应用到由混沌FHN神经元振子为动力节点所构成的一个具有近邻耦合结构的复杂动力网络,数值模拟表明了所获理论结果的正确性和控制方法的有效性.     

统计能量分析中的响应统计估计及其研究进展

统计能量分析(SEA)是分析复杂动态系统结构－声耦合振动响应的有效方法,而结构响应的统计估计是评价SEA分析准确性的基本依据,是SEA的一个重要组成部分.在简要介绍了SEA基本理论及其响应统计估计理论的基础上,对SEA中的响应统计估计的研究进展进行了综述和讨论,指出了在SEA响应统计估计中存在的问题,论述了需要进一步深入研究的方面,并着重讨论了响应统计估计中基于Poisson频率空间和高斯正交总体(GOE)频率空间的结构响应方差分析方法及其在SEA响应统计估计发展中的重要作用.      

基于无网格—图论方法的岩体边坡稳定性分析研究

将无网格伽辽金法应用于岩体边坡稳定性分析,发展了基于无网格模型和有向加权图Bellman-Ford最短路径搜索算法相结合的无网格-图论边坡滑移面搜索方法,以搜寻节理岩体边坡失稳时的临界滑移面并得出其相应的安全系数.区别于传统的滑移面搜索算法,本文方法无需假定滑移面形状,更适用于具有复杂滑移线形状的节理岩体边坡的稳定性分析与计算,具有稳定和高效的算法特点.文中详细论述了无网格-图论最短路径算法的理论、方法和程序实现,并通过算例说明该方法在岩体边坡稳定性分析中的适用性.     

螺旋波动力学及其控制

螺旋波是时空斑图结构演化的一个典型研究对象,无论从理论研究意义还是从应用价 值来看都是非常重要的,它可涉及到的领域包括:数学、物理、力学、天文、化学、生物、 医学等学科. 本文较为详细地讨论了螺旋波的动力学行为, 主要包含以下几方面: 螺旋波的 形成、螺旋波的几种常见的形式、螺旋波波头的运动、螺旋波失稳方式等. 由于螺旋波及其 破碎后的行为在许多具体的系统中的有害作用, 本文也介绍了螺旋波的几种控制方案: 反馈 控制方案、外力控制方案、调整参数控制方案等.     

基于无网格一图论方法的岩体边坡稳定性分析研究

将无网格伽辽金法应用于岩体边坡稳定性分析,发展了基于无网格模型和有向加权图Bellman—Ford最短路径搜索算法相结合的无网格-图论边坡滑移面搜索方法,以搜寻节理岩体边坡失稳时的临界滑移面并得出其相应的安全系数。区别于传统的滑移面搜索算法,本文方法无需假定滑移面形状,更适用于具有复杂滑移线形状的节理岩体边坡的稳定性分析与计算,具有稳定和高效的算法特点。文中详细论述了无网格-图论最短路径算法的理论、方法和程序实现,并通过算例说明该方法在岩体边坡稳定性分析中的适用性。     

基于BP网络的地磁基准图制备及其精度评价

利用测量数据建模和插值是地磁基准图制备的两种基本方法,常用的地磁场建模方法不适合小尺度的区域地磁场建模.人工神经网络具有良好的逼近任意复杂非线性系统的能力,本文引入应用最为广泛的反向传播(Backward Promulgation,BP)神经网络建立区域地磁场的模型,将地理经度和纬度作为输入,地磁场总强度值作为输出,通过部分测量数据对网络进行训i练,用其余测量数据对网络的性能进行评价,进而由训练好的网络得到基准图制备需要的地磁数据.分别使用BP网络建模方法和8种插值方法在不同数据点分布情况下进行了基准图的制备实验,精度评价结果表明了BP网络建模方法的有效性.根据实验结果对不同数据点分布情况下各种方法的优劣进行了比较.     

全息干涉条纹图的计算机自动处理与识别

本文应用数字图象处理与识别技术在IBM-PC/AT微处理计算机图象处理系统上对复杂的全息干涉条纹图进行了自动分析,文中采用二维灰度值检测的方法获取条纹的准峰或谷值二值图形,然后通过细化得到条纹中心,提出了用记忆跟踪算法自动去除毛刺和噪声线段.在用光标进行人机对话标定零级条纹后,可自动识别出其它整数条纹级数.分数级条纹级数可在整数级条纹数据之间进行线性或非线性插值得到.最后给出了全息条纹图分析的实例.     

材料破坏过程中应力分布的数值光弹图

 介绍应用材料破坏过程分析(MFPA)系统进行材料破坏过程应力 场分析的“数值光弹”方法. 给出了几种材料试样在外部载荷作用 下变形或破坏时的内部应力分布条纹图. 结果表明(MFPA)系统为研 究材料破坏过程中的应力分布提供了一种简单易行的分析方法.     

复杂网络上的博弈

博弈理论在社会、经济、生物以及生态等系统中存在着广泛的应用,复杂网络理论则是研究复杂系统全新而有力的工具,因此将博弈理论与复杂网络理论相结合成为研究复杂系统一个新的热点.概述国内外当前关于复杂网络上博弈动力学的研究情况和发展动态,包括基本的博弈模型、主要关注的问题、以及网络结构和博弈动力学的相互作用等,最后探讨进一步的研究课题.      

Synchronized regions of pinned complex networks: spectral analysis

The synchronization problem for a complex dynamical network is investigated in this paper from a spectral analysis approach. It is assumed that only a small portion of the nodes in the network are chosen to be controlled, known as the pinning control scheme. Some new types of synchronized regions for networks with different node dynamics and inner-coupling structures are discovered, especially for the case of the special chaotic node systems with a stable equilibrium point under fully anti-diagonal and partially anti-diagonal couplings. The eigenvalue distributions of the coupling and control matrices for different types of complex networks are obtained. The effects of the network topology, global coupling strength, pinning density, and pinning strength on the network synchronizability are examined through extensive numerical simulations. It is shown that the synchronizability of the pinned network can be effectively improved by increasing the overall coupling strength, pinning density, and pinning strength for some classes of synchronized regions, whereas too large the pinning density and pinning strength will lead to desynchronization for other classes. It is found that small-world networks are not always easier to synchronize than regular rings, and a denser eigenvalue distribution may not always imply better synchronizability.     

Synchronization in complex dynamical networks with interval time-varying coupling delays

This paper deals with the synchronization problem of complex dynamical networks with interval time-varying coupling delays. A simple local linear feedback controller is introduced to guarantee the synchronizability of the networks. Some delay-dependent synchronization conditions for the controlled complex dynamical networks are presented by using the Lyapunov–Krasovskii functional method and the reciprocally convex combination approach. Theoretical analysis and numerical examples show that the obtained conditions have less computational complexity and less conservatism than some recently reported ones.     

Synchronization properties of interconnected network based on the vital node

In this paper, we perform an intensive study of the synchronization properties of interconnected network and the concepts of vital node, and the simplest and equivalent network is firstly introduced. We strictly derive the eigenvalues of Laplacian matrix and the synchronizability of interconnected network and its simplest and equivalent network through utilizing the master stability function approach. Firstly, we find the synchronizability of interconnected network is identical to its simplest and equivalent network. Secondly, we identify the general factors that determine the synchronizability of interconnected network and further analyze the impact of different factors on the synchronizability. Finally, theoretical analysis and numerical simulations are carried out to indicate the validity and effectiveness of current analysis. The current results are beneficial to understand the dynamical behaviors of complex networked systems.     

Exponential synchronization for second-order nonlinear systems in complex dynamical networks with time-varying inner coupling via distributed event-triggered transmission strategy

This paper focuses on the exponential synchronization problem of complex dynamical networks (CDNs) with time-varying inner coupling via distributed event-triggered transmission strategy. Information update is driven by properly defined event, which depends on the measurement error. Each node is described as a second-order nonlinear dynamic system and only exchanges information with its neighboring nodes over a directed network. Suppose that the network communication topology contains a directed spanning tree. A sufficient condition for achieving exponential synchronization of second-order nonlinear systems in CDNs with time-varying inner coupling is derived. Detailed theoretical analysis on exponential synchronization is performed by the virtues of algebraic graph theory, distributed event-triggered transmission strategy, matrix inequality and the special Lyapunov stability analysis method. Moreover, the Zeno behavior is excluded as well by the strictly positive sampling intervals based on the upper right-hand Dini derivative. It is noted that the amount of communication among network nodes and network congestion have been significantly reduced so as to avoid the waste of network resources. Finally, a simulation example is given to show the effectiveness of the proposed exponential synchronization criteria.     

Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes

A fractional-order weighted complex network consists of a number of nodes, which are the fractional-order chaotic systems, and weighted connections between the nodes. In this paper, we investigate generalized chaotic synchronization of the general fractional-order weighted complex dynamical networks with nonidentical nodes. The well-studied integer-order complex networks are the special cases of the fractional-order ones. Based on the stability theory of linear fraction-order systems, the nonlinear controllers are designed to make the fractional-order complex dynamical networks with distinct nodes asymptotically synchronize onto any smooth goal dynamics. Numerical simulations are provided to verify the theoretical results. It is worth noting that the synchronization effect sensitively depends on both the fractional order ?? and the feedback gain k _i . Moreover, generalized synchronization of the fractional-order weighted networks can still be achieved effectively with the existence of noise perturbation.     

Discontinuous synchrony in an array of Van der Pol oscillators

We show the phenomenon of complete synchronization in an network of coupled oscillators. We confirm that non-diagonal coupling can lead to the appearance or disappearance of synchronous windows (ragged synchronizability phenomenon) in the coupling parameter space. We also show the appearance of clusters (synchronization in one or more group) between coupled systems. Our numerical studies are confirmed by an electronic experiment.     

软件系统的复杂网络研究进展

互联网给软件带来了革命性的转变------软件网络化,这种趋势使软件作为全局性的资源,以网络为媒介向大众用户提供各种信息资源的应用服务.软件的计算模式、应用模式、产品形态以及盈利模式都会发生很大的变化,例如今后软件的应用方式就像打电话一样, 通过网络租用软件来实现.网络化软件正会成为联接各种网络资源、数据资源、计算资源的核心,成为数据和数据交换的基础. 同时, 网络化软件系统也将成为复杂系统,而复杂性也是软件开发困难、质量难以保证的关键.软件工程是将系统化、规范化、可度量的方法应用于软件的开发、运行和维护.复杂网络理论的最新研究成果,为复杂系统的软件工程提供了新的数学基础和方法. 分析了软件的复杂性,介绍了复杂网络与软件复杂性结合的研究工作,包括软件系统的拓扑特性、形成机理、演化规律以及软件复杂性度量和评估,对软件网络的研究现状进行了小结, 并列举了需要进一步研究的问题.提出软件网络观(软件在网络中生长、可以用网络来刻画软件)将有助于我们深入理解和认识软件的复杂性本质.      

Projective and lag synchronization between general complex networks via impulsive control

This paper mainly investigates the projective and lag synchronization between general complex networks via impulsive control. A general drive complex network and an impulsively controlled slave network are presented in the model. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. Some criteria and corollaries are, respectively, derived for the projective synchronization and lag synchronization between the presented impulsively controlled complex networks. Finally, the results are illustrated by complex networks composed of the chaotic Lorenz systems. All the numerical simulations verify the correctness of the theoretical results.     

Nonlinear synchronization on connected undirected networks

In this paper, we give sufficient conditions to have a complete synchronization of oscillators in connected undirected networks. The oscillators we are considering are not necessarily identical and the synchronization terms can be nonlinear. Many results in the literature deal with sufficient conditions insuring complete synchronization. This is a difficult problem since such conditions require to take into account the individual dynamics of the oscillators and also the graph topology. In this paper, we extend one of these results, the connection graph stability method, to nonlinear coupling functions and we also give an existence condition of trajectories of the oscillators. The sufficient conditions for synchronization presented in this paper are based on the study of a Lyapunov function and on the use of pseudometrics which enable us to link network dynamics and graph theory. These results are applied to a network of Chua’s oscillators and lead to an explicit condition insuring the complete synchronization of the oscillators.     

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures

Spatiotemporal chaos synchronization between uncertain complex networks with diverse structures is investigated. The identification law of unknown parameters and the adaptive law of the configuration matrix element in state equations of network nodes are determined based on stability theory, and the conditions of realizing spatiotemporal chaos synchronization between uncertain complex networks with different structures are discussed and obtained. Further, the Fisher–Kolmogorov system with spatiotemporal chaotic behavior is taken as the nodes of drive and response networks to imitate the experiment. It is found that the synchronization performance between two networks is very stable.