摘要
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。
This review article tries to systematically summarize and review important progreses in dynamical complexity of nonlinear networks, which is a key project supported by the NSFC. The theory, demonstration and application of complex networks have innovativeness and distinguished features. Three monographs and more than 120 SCI and 15 EI articles are published. Characteristics of complexity and quantitative features of complex networks are revealed profoundly. A unified hybrid network theoretical frame is set up, including three theoretical models and a network complexity pyramid. Another family of complex network---generalized Farey tree network--and its organized pyramid are introduced. It is found that transition relations exist between complexity-simplicity and diversity-universality. The relationship between topological properties and dynamical behaviours is revealed. Partial （generalized） synchronization in reguler network models with a few shoutcuts is investigated and partial synchronization criterion is proposed, which is further applied to synchronize spatiotemporal systems with sparse connections. Several models, methods and ways for improving synchronizability are proposed, which are associated with topological characteristic quantitaties, optimal synchronization, synchronization prefirential,various weights and influence of leaf nodes. Multi-objective control strategies in different subnetworks for chaotic connected networks are suggested. Synchronization and control of beam halochaos in beam transport network with small-world （BTN-SW） and bean transport network with scale-free （BTN-SF） are realized by new methods. Adaptive velocity model for swarm aggregation is proposed, which provides a powerful mechanism in biological and technological multiagent systems. The trafficrouting control and gaming of resource competition on the Internet are researched. Some spreading laws on different kinds of networks are explored. The evolution features of weighted economic scientist cooperation network are studied. High-tech networks with 4 levels and large online social networks are investigated. Furthermore, a non-equilibrium statistical method is suggested, and macroscopic network is promoted toward microscopic networks（quantum information and nano inference networks）. In the past 4 years,we have organized and attended a number of academic conferences at home and abroad. 38 graduate students and PhD students graduated.
出处
《物理学进展》
CSCD
北大核心
2009年第1期1-74,共74页
Progress In Physics
基金
国家自然基金项目(批准号:70431002)
面上项目与理论物理专项项目(批准号:60874087
10647001)
关键词
非线性网络
动力学复杂性
统一混合理论框架
网络金字塔
同步与控制
拥塞与博弈
多智能体网络
束流输运网络
高科技网络
社会网络
微观网络
Nonlinear network
dynamical complexity
unified hybrid network theory framework
complexity pyramid
synchronization and control
multi-intelligent agent networks
beam transport network
high-tech network
social network
micronetwork
