复杂网络上的振荡斑图动力学的研究

项目名称： 复杂网络上的振荡斑图动力学的研究

项目编号： No.11205041

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 物理学II

项目作者： 廖旭红

作者单位： 杭州师范大学

项目金额： 22万元

中文摘要： 复杂网络在社会系统、生物系统等领域得到广泛应用，脑网络就是一个典型的例子。脑中神经活动存在丰富的节律振荡。这些振荡的功能与产生机制尚不明确，但是种种迹象表明振荡的时空斑图与脑的信息处理紧密相关。研究复杂网络上振荡行为的时空斑图以及形成机制对于理解包括脑在内的复杂系统的功能有重要意义。本项目研究复杂网络上的振荡斑图动力学，包括可激发复杂网络上自持续振荡的理论研究，以及脑网络上自发活动的动力学的实证分析。在理论研究中，我们将考察可激发复杂网络上自持续振荡的可能斑图类型和形成机制，并寻找影响系统动力学的关键因素，对振荡进行有效调控；在实证分析中，我们将结合神经影像数据，分析人脑网络上血氧活动信号的自发振荡的动力学规律，并借鉴前期理论研究成果探讨脑网络上可能的斑图形态及自组织过程。这些研究将有利于人们进一步认识复杂系统中宏观行为和协同性涌现的微观机制，对理解脑的功能组织原则也有所启发。

中文关键词： 复杂网络；斑图动力学；自持续振荡；脑网络；结构-功能关联

英文摘要： Complex networks of coupled dynamical systems offer a general framework to study social and biological systems, among which the brain network is a typical example. Oscillatory neural activity is ubiquitous in the brain. A number of recent experiments have pointed the possible roles of propagation waves in olfaction, visual perception, audition and memory formation, which indicate that the spatiotemporal patterns of oscillations in the brain are important. Till now the underlying mechanism of both oscillation generation and wave propagation in the brain is not yet clear. This project aims to study the dynamics of pattern formation of oscillations in complex networks, including a theoretical study on self-sustained oscillations in excitable complex networks, as well as a demonstration analysis of spontaneous activities in the human brain network. The project is divied into two parts. First, we will study self-sustained oscillations in complex networks consisting of excitable nodes and investigate the dynamics of pattern formation. We will unveil different kinds of spatiotemporal patterns, identify their oscillation sources, display the wave propagation paths and explore the topological effects on network oscillations. Then based on the mechanism revealed, we will modulate the oscillations efficiently. Second, base

英文关键词： Complex networks；Pattern dynamics；Self-sustained oscillations；Brain networks；Structure-function relationship