基于动态优化策略的复杂网络研究

项目名称： 基于动态优化策略的复杂网络研究

项目编号： No.60804046

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 陈茂银

作者单位： 清华大学

项目金额： 19万元

中文摘要： 基于动态优化策略，本项目将研究多种情况下复杂网络上的完全同步或相位同步，并在基础上分析网络同步倾向、以及大规模复杂网络结构和功能之间的关系。主要研究内容包括：(a) 针对小世界或无标度网络，基于动态优化策略，提出一种统一的、代价较小的自适应调整权重方法，不仅能够实现多种情况下的完全同步或相位同步，而且能够保证在网络的同步过程中所有节点具有相同的强度。(b) 针对小世界或者无标度网络，通过多种情况下的完全同步或相位同步配置网络中的耦合作用矩阵，使网络具有比已有自适应调整权重方法更好的同步倾向，并进一步分析同步倾向、连接权重、拓扑结构之间的关系。(c) 针对具有不同社团的复杂网络或具有复杂连接的大规模猫脑皮层神经网络，基于动态优化策略自适应调整权重，探讨网络结构与网络功能之间的关系。这项研究不仅有助于理解复杂网络结构和动力学之间的关系，而且有助于理解大规模复杂网络结构与功能之间的关系。

中文关键词： 复杂网络；小世界网络；无标度网络；同步；同步倾向

英文摘要： Based on the dynamic optimization strategy, we will study the synchronization in complex networks, analyze the synchronizability of networks, and then discuss the relationship between network structures and functions. We mainly studied the following topics. (a) For scale-free or small-world networks, we proposed an unifying adaptive weight approach, which not only ensures complete synchronization or phase synchronization in different types of networks, but also realize the uniform intensities for all the nodes during the path to synchronization.(b) For scale-free or small-world networks, we also studied the synchronizability by adaptively adjusting the weights of incoming links through the dynamic optimization strategy. In addition, the above newtorks have the better synchronizability. (c) We discussed the the response of scale-free networks with community structure to external stimuli. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topologicalcommunities.

英文关键词： complex networks; samll-world networks; scale-freee networks; synchronization; synchronizability