复杂网络动力学的几个分岔与混沌问题的研究

项目名称： 复杂网络动力学的几个分岔与混沌问题的研究

项目编号： No.10872119

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 李常品

作者单位： 上海大学

项目金额： 36万元

中文摘要： 复杂网络动力学是非线性动力学中的一个新近出现的活跃分支，目前复杂网络动力学的研究内容大部分集中在网络同步、网络建模、网络计算与分析等方面。本项目的研究内容正是按这些方面展开的，具体说来，研究成果包括：1）耦合网络间的同步与反同步。研究了离散耦合网络间的同步、时滞离散网络间的外同步、时滞连续网络间的外同步、耦合网络间的反同步。2）时滞网络的内同步。研究了具有无标度效应的时滞网络的内同步、带双重时滞和非线性耦合网络的内同步。3）确定性网络的建模与拓扑分析。研究了小世界特性和无标度效应的科赫网络的演化模型、确定性时滞拟分形网络模型。4）随机网络模型与分析。研究了BA网络和LCD网络的稳定性，用马尔科夫迭代方法研究了增长网络的度分布。此外开辟了分数阶动力学这一新的研究方向。这些研究使我们对复杂网络动力学、分数阶动力学有了更深刻的认识，所得成果丰富了复杂网络动力学的研究内容并掀起了分数阶动力学的研究热潮。项目执行期间，共有9名硕士生、5名博士生毕业，共发表SCI收录文章24篇，主持出版SCI专辑一期，高等教育出版社出版专著一部，获上海市自然科学三等奖一次（第一完成人），获宝钢优秀教师奖一次。

中文关键词： 复杂网络；同步；时滞；网络拓扑；分数阶动力学

英文摘要： Dynamics of complex network is a newly active branch in nonlinear dynamics. Network synchronization, network modeling and network computation with analysis are main topics in the studies of complex network. The main contents in this program include: 1) synchronization and anti-synchronization between two coupled networks which cover discrete-time and continuous-time case with or without delays, 2) synchronization inside a network focus on the delay case with scale-free interactions and the double time delays with nonlinear inner-coupling functions, 3) deterministically network and its topological analysis which deal with the delayed pseudo-fractal networks and small-world scale-free Koch networks, 4) stochastic network modeling and its analysis which contain the stability of BA network and LCD network, and stochastic analysis for the network. Besides, we find a new research topic-fractional dynamics. All this helps us to deeply understand the dynamics of complex network and fractional dynamics. This challenging and exciting topic will offer fresh stimuli for the fractional calculus community to further promote and develop the cutting-edge research on fractional dynamics and its numerical simulation. By the financial support of this project, we have published 26 SCI papers. And we have brought up 9 master students and 5 Ph D students who have earned their degrees. I, as a guest lead editor, have a special issue in an SCI journal. The co-investigator has published one book in Higher Education Press. I was awarded the third prize of Shanghai Natural Sciences and Bao Steel Prize.

英文关键词： complex network；synchronization；time delay； network topology；fractional dynamics