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网络科学与工程丛书:复杂网络协调性理论

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网络科学与工程丛书:复杂网络协调性理论

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协调性是复杂网络研究中的一类重要课题,是对复杂网络中一类动力学行为的概括,其本质是网络通过局部个体之间的相互作用实现整体的协调。《网络科学与工程丛书:复杂网络协调性理论》对复杂网络的协调性行为作了系统、全面和深层次的阐述,建立了一个统一的数学框架,把协调性行为放在不变Riemann子流形横向稳定性平台上进行研究。全书共10章,主要内容包括:复杂网络与复杂系统,数学准备,协调性与横向稳定性理论,耦合微分动力系统的同步,耦合映射网络的同步,复杂网络的同步能力,分群同步,多主体网络的一致性,复杂网络的牵引控制,总结、比较和讨论。
《网络科学与工程丛书:复杂网络协调性理论》内容丰富、理论严谨、概念清晰,澄清了耦合网络协调性中的一些认识误区,有助于复杂性科学与网络科学等领域的研究。《网络科学与工程丛书:复杂网络协调性理论》可作为相关学科研究生的教材,亦可作为相关领域研究者的参考手册。
Author Description

陈天平,复旦大学教授、博士生导师。1965年复旦大学数学系研究生毕业,师从著名数学家陈建功教授。1985年起为复旦大学教授。
在包括神经网络、非线性映照理论、盲信号分离、主成分分析、复杂网络等研究方面做出了突出的贡献。曾获2002年度国家自然科学奖二等奖,1998年度上海市科技进步奖一等奖,1998年度教育部科技进步奖一等奖,1997年度IEEE Transaction on Neural Networks杰出论文奖,1997年度日本神经网络学会最佳论文奖。所培养的多名博士生获上海市优秀博士论文奖,一人获全国优秀博士论文奖。

卢文联,1978年出生,复旦大学数学专业学士(2000年)和应用数学专业博士(2005年)。2005-2007年,德国马克斯普朗克科学数学研究所博士后。现为复旦大学数学科学学院应用数学系教授,2012年作为欧盟委员会资助的玛丽一居里学者访问英国Warwick大学计算机系。2007年获全国百篇优秀博士论文奖,2008年获上海是自然科学二等奖(第二完成人),2011年获得亚太神经网络协会“青年研究者奖”。现担任IEEE Transactions on Neural Networks and Learning Systems(2013-)和Neuocomputing(2009-)编委,以及International Journal on Bifurcation and Chaos(2010-)客座编委。研究方向包括:神经网络模型的数学方法及其应用、复杂系统与复杂网络理论和应用、非线性动力系统、计算神经模型和大脑影像数据处理等。
Catalogue

符号表

第一章 复杂网络与复杂系统
1.1 复杂网络的理论和模型
1.2 协调性行为
参考文献

第二章 数学准备
2.1 代数图理论和矩阵理论
2.2 具有不连续右端的微分方程
2.3 随机过程与随机动力系统
2.4 耦合复杂网络动力学模型
参考文献

第三章 协调性与横向稳定性理论
3.1 不变子流形的横向稳定性
3.1.1 确定性动力系统的横向稳定性
3.1.2 随机动力系统的横向稳定性
3.2 李亚普诺夫方法
参考文献

第四章 耦合微分动力系统的同步
4.1 线性耦合微分动力系统的同步
4.1.1 局部同步性
4.1.2 全局同步性
4.2 时滞的影响
4.2.1 时滞耦合系统局部同步
4.2.2 时滞耦合系统全局同步
4.3 非线性耦合动力系统的同步
参考文献

第五章 耦合映射网络的同步
5.1 耦合映射网络的同步分析
5.2 时变切换映射网络的同步
参考文献

第六章 定义复杂网络的同步能力
6.1 复杂网络的同步能力
6.2 网络拉普拉斯矩阵谱的分析
6.3 时变耦合拓扑结构的同步能力
6.4 自适应反馈算法
参考文献

第七章 分群同步
7.1 耦合微分方程的全局分群同步
7.2 分群同步方案
7.3 基于自适应反馈的分群同步算法
7.4 耦合映射网络的分群同步
参考文献

第八章 多主体网络的一致性
8.1 静态耦合多主体网络的一致性
8.1.2 随机切换拓扑结构的网络多主体系统的一致性
8.3 通信时滞的影响
8.3.1 具有时变时滞的连续系统一致性算法
……
第九章 复杂网络的牵引控制
第十章 总结、比较和讨论

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