网络科学中统一混合理论模型的若干研究进展

复杂网络的理论模型研究一直是网络科学的最重要课题之一.首先概述网络科学理论发展史上的3个里程碑以及有权演化网络的发展概况.为了全面反映确定性与随机性混合的真实世界的统一性、多样性和复杂性,使网络理论模型更加接近实际网络的全面特性,着重评述近年来发展的统一混合网络理论模型的3部曲:和谐混合择优模型、统一混合网络模型和统一混合变速增长网络模型,总结和评述了混合理论模型3部曲的不同特点和相互联系,揭示了统一混合网络的复杂性与普适性及其错综复杂的转变关系.最后指出, 该理论在多层次高科技网络等实际网络中的应用前景.      

复杂网络研究的一些统计物理学方法及其背景

介绍近年来复杂网络研究中常用的几种统计物理学方法（平均场理论、主方程、率方程、生成函数）的物理背景、发展历史、观点、思想和方法.回顾了物理学在研究连续相变、自组织临界现象、流行病传播等问题时是如何发展、运用平均场理论,以及平均场理论的思想、方法在从平衡态向非平衡态研究的延伸过程中的演化过程.简介了主方程、率方程和生成函数的相关物理思想和概念.在最后一节介绍了一些运用这些方法研究复杂网络的成果,包括一些最著名以及值得注意的网络演化模型的平均场方法、主方程和率方程方法求解,一些网络统计性质的解析求解,以及一些网络上物理过程特征描述的解析分析等.      

系统科学方法论探索

众所周知,系统科学是适应科学方法论的变革而产生的新学科。系统科学研究自然界和人类社会各类复杂系统的共同特性,探索系统的生成、演化和涌现的普遍规律。系统科学与经典科学在方法论上有着本质的区别。经典科学注重还原分析,而系统科学强调整体把握。本文首先回顾我国在系统科学方法论上所取得的重要成果,接着简介作者从运筹学角度对描述方法所做的研究,然后着重探讨网络科学的研究方法对系统科学的借鉴作用。      

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.      

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.      

复杂脑网络研究进展

复杂网络的研究方法是近年来对生物网络、社会网络及技术网络等真实网络进行研究的新兴方法.利用这一方法,可以从大脑皮层结构性网络、功能性网络以及效率性网络等不同角度着手对大脑的功能性分割和功能性整合两个主要功能进行研究,并进一步讨论其生长和发展演化,以期揭示支配大脑运作的规律.      

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.      

神经系统疾病与认知动力学 (I) : 癫痫发作的动力学与控制

研究表明癫痫发作过程与神经系统本身的非线性动力学行为密切相关. 因此, 开展癫痫发作的非线性网络动力学建模与调控问题的研究, 有助于理解癫痫临床表征的动力学机理和定位致痫灶网络, 进而设计有效的网络调控策略. 本文回顾了癫痫脑神经疾病网络动力学与控制方面的研究进展, 系统总结了本文作者近年来在癫痫发作动力学建模分析及其调控等方面取得的研究成果. 首先, 基于海马齿状回CA3区环路神经元网络模型, 分析了影响颞叶癫痫发作的分子和网络结构因素, 阐释了癫痫发作转迁的动力学机制. 其次, 由于脑神经系统的集群编码特性, 基于神经场模型和平均场模型建模方法完善了皮质?基底节?丘脑环路网络动力学理论框架, 并基于此框架分析了失神癫痫发作转迁的动力学分岔机制, 探讨了不同类型癫痫发作的转迁路径, 发现了失神癫痫发作转迁的多稳态共存现象, 揭示了时滞对失神癫痫同步发作的控制效果, 设计了丰富有效的癫痫深脑刺激调控策略, 给出了电刺激调控失神癫痫发作的动力学解释. 最后, 通过数据驱动的统计建模和神经元群模型动力学建模分析, 提出了局灶癫痫致痫灶定位及寻找有效控制癫痫发作网络关键节点的理论新方法. 这些研究成果为理解难治性癫痫发作动力学本质及在临床诊疗的应用方面提供重要理论支撑. 最后对进一步研究给出若干建议.      

直升机结构动特性建模技术研究

在直升机设计阶段通过建模分析进行全机动特性设计,准确地预测全机振动响应是控制和降低直升机振动水平的关键技术,本文以某直升机为研究对象,对机体结构的动特性建模技术进行了深入的研究.采用从部件到全机建模的研究策略,把整个机体分成尾段、舱门、机身段,分别进行有限元建模、动特性试验、相关分析、模型修改技术和建模准则的研究.在此基础上,对部件连接界面建模分析,组装修改后的各部件模型,建立全机动特性分析模型.通过对该机动力学建模、试验相关分析与模型修改,大大增强了分析模型的预测能力,达到了40Hz以内的频率误差小于11%的预测精度,突破了对直升机复杂结构建模关键技术,建立了适用于直升机结构动力学分析的建模准则,在该机动特性设计中取得了成功.     

复杂动态网络控制研究进展

研究复杂网络结构性质与模型的主要目的之一就是为了了解网络结构与网络功能之间的关系,并在此基础上考虑改善网络性能的有效途径.综述了近年关于利用分布式控制的方法使得一个动态网络具有期望行为的一些研究进展.对于具有固定和连通的拓扑结构的复杂动态网络,牵制控制策略的有效性与网络拓扑密切相关.综述了牵制控制的可行性、稳定性分析以及控制策略比较研究. 另一方面,对于具有时变拓扑结构的动态网络的控制,着重综述了移动多自主体网络系统的蜂拥控制,并特别阐述了如何把牵制控制的思想用于蜂拥控制.      

Stochastic phase decoupling in dynamical networks

Network models and their theories play a central role in the understanding of complex systems, in particular complex social systems such as societies and organizations. An important problem is to understand how agent attributes become organized within the connectivity structure of a network. The effective matching of agent attributes is important for the expression of functionality by a network. The creation of static networks relative to some control parameter has been extensively studied and gives rise to order-disorder phase transitions. This paper extends this work to dynamic networks. Several models of dynamic networks are created relative to two control parameters and their associated stochastic phase transitions are examined. Under conditions of weak coupling between the control parameters, it is shown that the relevant stochastic phase transitions become decoupled from one another, each qualitatively distinct and dependent on a single (distinct) control parameters.     

Synchronization in a fractional-order dynamic network with uncertain parameters using an adaptive control strategy

This paper studies synchronization of all nodes in a fractional-order complex dynamic network. An adaptive control strategy for synchronizing a dynamic network is proposed. Based on the Lyapunov stability theory, this paper shows that tracking errors of all nodes in a fractional-order complex network converge to zero. This simple yet practical scheme can be used in many networks such as small-world networks and scale-free networks. Unlike the existing methods which assume the coupling configuration among the nodes of the network with diffusivity, symmetry, balance, or irreducibility, in this case, these assumptions are unnecessary, and the proposed adaptive strategy is more feasible. Two examples are presented to illustrate effectiveness of the proposed method.     

A novel deterministic hybrid complex network model created by inner–outer iteration

Complex networks are ubiquitous in real-life systems. Most previous models of complex networks are stochastic. In order to decrease the randomness and make it more direct to gain a visual understanding on complex network evolving mechanism, we present a deterministic algorithm that generates a hybrid network model with the characteristics of small-world networks and random networks. In this model, the network growth is determined by triangle inner and outer node and edge iterations. We analyze the main topological properties by both theoretical predictions and numerical simulations. The results show that our growing model has a low average path length, a high clustering and an exponential degree distribution.     

生物神经网络系统动力学与功能研究

生物神经系统是由数量极其巨大的神经元相互联结的信息网络系统,在生物体的感觉、认知和运动控制中发挥关键性的作用.首先介绍神经元、大脑和一些生物神经网络的生理结构和理论模型,然后分别介绍其放电活动和网络动态特性的一些重要问题,包括神经元的复杂放电模式、耦合神经元网络系统的同步活动和时空动力学、大脑联合皮层神经微回路的网络结构特征,以及工作记忆和抉择过程的动力学机制等. 最后对今后研究给出一些展望.      

Global synchronization of stochastic delayed complex networks

This paper is concerned with the delay-dependent synchronization criterion for stochastic complex networks with time delays. Firstly, expectations of stochastic cross terms containing the It? integral are investigated by utilizing stochastic analysis techniques. In fact, in order to obtain less conservative delay-dependent conditions for stochastic delay systems including stochastic complex (or neural) networks with time delays, how to deal with expectations of these stochastic cross terms is an important problem, and expectations of these stochastic terms were not dealt with properly in many existing results. Then, based on the investigation of expectations of stochastic cross terms, this paper proposes a novel delay-dependent synchronization criterion for stochastic delayed complex networks. In the derivation process, the mathematical development avoids bounding stochastic cross terms. Thus, the method leads to a simple criterion and shows less conservatism. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.     

图论与复杂网络

近10年来迅猛发展起来的复杂网络理论为研究复杂性与复杂系统科学提供了一个重要支撑点,它高度概括了复杂系统的重要特征,无论是在理论还是在应用方面都具有很强的生命力,而且在各个方面都得到了很大发展.重点讨论图论在复杂网络中的应用,特别是代数图论在复杂网络同步问题中的应用.首先给出一些图的最小非零与最大特征值以及同步能力的估计,并且讨论了子图与图特征向量在同步能力估计中的作用.其次以两个简单图指出同步能力与网络结构参数的关系复杂,并给出补图与加边对同步研究的意义,然后给出图运算在复杂网络同步中的作用.最后从图论与控制理论角度展望了复杂网络领域未来可能的发展方向.      

Stochastic Pore Network Generation from 3D Rock Images

Pore networks can be extracted from 3D rock images to accurately predict multi-phase flow properties of rocks by network flow simulation. However, the predicted flow properties may be sensitive to the extracted pore network if it is small, even though its underlying characteristics are representative. Therefore, it is a challenge to investigate the effects on flow properties of microscopic rock features individually and collectively based on small samples. In this article, a new approach is introduced to generate from an initial network a stochastic network of arbitrary size that has the same flow properties as the parent network. Firstly, we characterise the realistic parent network in terms of distributions of the geometrical pore properties and correlations between these properties, as well as the connectivity function describing the detailed network topology. Secondly, to create a stochastic network of arbitrary size, we generate the required number of nodes and bonds with the correlated properties of the original network. The nodes are randomly located in the given network domain and connected by bonds according to the strongest correlation between node and bond properties, while honouring the connectivity function. Thirdly, using a state-of-the-art two-phase flow network model, we demonstrate for two samples that the rock flow properties (capillary pressure, absolute and relative permeability) are preserved in the stochastic networks, in particular, if the latter are larger than the original, or the method reveals that the size of the original sample is not representative. We also show the information that is necessary to reproduce the realistic networks correctly, in particular the connectivity function. This approach forms the basis for the stochastic generation of networks from multiple rock images at different resolutions by combining the relevant statistics from the corresponding networks, which will be presented in a future publication.     

Adaptive neural network control for coordinated motion of a dual-arm space robot system with uncertain parameters

Control of coordinated motion between the base attitude and the arm joints of a free-floating dual-arm space robot with uncertain parameters is discussed. By combining the relation of system linear momentum conversation with the Lagrangian approach, the dynamic equation of a robot is established. Based on the above results, the free-floating dual-arm space robot system is modeled with RBF neural networks, the GL matrix and its product operator. With all uncertain inertial system parameters, an adaptive RBF neural network control scheme is developed for coordinated motion between the base attitude and the arm joints. The proposed scheme does not need linear parameterization of the dynamic equation of the system and any accurate prior-knowledge of the actual inertial parameters. Also it does not need to train the neural network offline so that it would present real-time and online applications. A planar free-floating dual-arm space robot is simulated to show feasibility of the proposed scheme.