关于非完全同步复杂网络中动力学问题的研究

项目名称： 关于非完全同步复杂网络中动力学问题的研究

项目编号： No.10805038

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 生物科学

项目作者： 王新刚

作者单位： 浙江大学

项目金额： 18万元

中文摘要： 由于其丰富的物理内容以及重要的应用意义，有关复杂网络同步的研究长期以来一直受到人们的关注。然而目前绝大多数的研究集中在网络的起始同步点或完全同步态上，而对存在于二者之间的大量的中间态所知甚少。本项目将从部分同步的角度，以斑图演化的方法对处于非完全同步状态下的复杂网络的动力学行为进行研究。研究的重点内容包括对非完全同步状态下的网络同步强度的量化、同步斑图的定义及其时空特征、复杂网络的退同步演化路径、网络的拓扑结构对斑图的结构以及网络退同步路径的影响等。该项研究将会极大的丰富我们对复杂网络动力学的认识，同时也将有助于我们解决很多实际复杂系统中所遇到的问题，如神经系统中模块功能的实现和计算网络中系统负载的分布等。

中文关键词： 复杂网络；混沌同步；时空斑图

英文摘要： Synchronization of complex networks has been a hot topic of modern physics for years, where the main objective is to disclose the interplay between the collective system dynamics and the underlying network topology. The current studies, however, focus on only two particular states of network synchronization: (1) The global synchronization state and (2) the onset state of synchronization; while the general case of non-synchronous states has been largely overlooked. These transition states, which are between the global synchronization and onset synchronization states, not only play an important role in disclosing the dynamical mechanisms of complex networks, but also represent the general case in practice. Here by this project, we shall systematically investigate the generally existed non-synchronous states in dynamical complex networks, where the topics to be studied include: (1) How to qualify the degree of synchronization in the non-synchronous region; (2) how to define the non-synchronous pattern; (3) what's the feature of the pattern evolution; (4) the path of network desynchronization; and (5) the influences of the network topology to the properties of the non-synchronous states. By these studies, we wish to have a global picture on the dynamics of complex networks, and could shed new light to the function and operation of many realistic systems which maintain their normal functions only in the non-synchronous states, e.g., the neural and the network computing systems.

英文关键词： Complex networks; Chaos synchronization; spatio-temporal pattern