时滞分形网络建模及其动力学分析

项目名称： 时滞分形网络建模及其动力学分析

项目编号： No.61203155

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 自动化学科

项目作者： 孙伟刚

作者单位： 杭州电子科技大学

项目金额： 24万元

中文摘要： 网络科学的诞生得益于网络理论模型（小世界模型和无标度模型）的突破性进展，而各种理论模型的研究仍然是最具挑战性课题之一，其中确定性网络也是一大类重要网络，与应用密切相关。本项目主要探讨确定性网络中实际普遍存在的但尚未研究清楚的时滞分形网络构建及其动力学的复杂性问题，探索时滞在模型构建中发挥的主要作用，同时研究随机游走与拓扑结构及同步能力之间的相互关系等。具体包括：首先提出一类时滞分形网络，寻求得到关于这类网络的一些网络量化指标的新方法及其精确结果，揭示时滞分形网络的统计规律性；其次导出平均首次到达时间、度分布的幂指数和网络拉普拉斯矩阵的特征值关于一些关键网络参数的精确解，以便分析网络的随机游走行为与度分布中的幂指数及随机游走与网络同步能力之间的相互关系；最后探讨这些研究的实际应用。此研究有助于理解一大类复杂系统的演化规律及可能应用，并为现实实际所需网络提供合理的设计与优化的理论指导。

中文关键词： 分形网络；时滞；随机游走；一致性；

英文摘要： Network science was born thanks to the breakthrough of network theorectical models (small-world model and scale-free model), while studies on various theorectical models are still one of the most challenging issues, among which deterministic networks are also important, and closely related to applications.This project mainly investigates the complexity of modelling and dynamics for delayed fractal networks, which are prevalent but have not been studied clearly among deterministic networks, discusses the effects of delays in the modelling, and investigates the relationships between random walks and topological strucutures, and even synchronizability. The contents of this project are as follows: firstly we propose a family of delayed fractal networks, and try to obtain new methods and exact results for some network quantities; secondly we obtain exact results of mean first passage time, power-law exponent in degree distribution and eigenvalues of Laplacian matrices with regard to critical network parameters through some fractal networks, which facilitates the studies on relationships between random walks and exponent of degree distribution and even synchronizability; finally we discuss applications of the obtained results. These studies may help with a deeper understanding the rules and possible applications of a

英文关键词： Fractal networks；delay；random walks；consensus；