两类复杂动力学网络的建模、分析与控制

项目名称： 两类复杂动力学网络的建模、分析与控制

项目编号： No.61463022

项目类型： 地区科学基金项目

立项/批准年度： 2015

项目学科： 自动化技术、计算机技术

项目作者： 吴召艳

作者单位： 江西师范大学

项目金额： 46万元

中文摘要： 复杂动力学网络是复杂性科学研究中最为广泛的研究方向之一，是研究大型现实复杂系统的有效工具。由于现实系统自身及个体之间相互作用的复杂性，需要建立更多的动力学网络模型以更好地描述现实世界。带有相同维数节点动力学的有色网络和一致超网络在我们的前期工作中已得到了初步研究。本项目将在前期工作的基础上基于图论中有色图和超图理论来研究两类动力学网络的建模、分析与控制。首先，建立更一般的有色网络模型，其节点动力学可以是不同维数的，并研究该类网络的同步与控制；其次，在已有一致超网络模型的基础上，建立能更好描述现实网络的一致演化超网络模型，并研究其上的同步与控制问题；再次，建立非一致演化超网络模型，分析这类网络的拓扑结构性质，进一步建立非一致动力学超网络模型并研究其同步与控制问题，重点研究网络牵制控制问题；最后，研究超网络的社团探测问题，给出社团探测的算法，进一步对现实超网络进行实证分析。

中文关键词： 复杂网络；系统建模；同步控制

英文摘要： Complex dynamical network is one of the most extensive field of research in the study of the complexity science, and an effective tools for studying large-scale real complex system. Due to the complexity of real systems themselves and the interactions among the individuals, more and more dynamical network models are needed to better describing the real world. In our previous works, colored network with identical-order nodes dynamics and uniform dynamical hyper-network have been preliminarily studied. According to the colored graph theory and hypergraph theory, this project will study the modelling, analysis and control of two class of dynamical networks bease on the previous works. Firstly, we construct a class of more genral colored dynamical networks and study the synchronization and control of them, in which the order of nodes dynamics can be different. Secondly, based on the existing hypernetwork models, we construct new uniform evolving hypernetwork models for better describing the real world and study the synchronization control problem. Thirdly, we construct nonuniform evolving hypernetwork models and analyze their topological properties. Further, we construct nonuniform dynamical hypernetwork models and study the synchronization and control problems, especially pinning control problem. Finally, we study the community detection of hypernetworks and provide several algorithms. Further, we do empirical analyses on some real hypernetworks.

英文关键词： complex network;system modelling;synchronization control