复杂网络上的振荡斑图动力学的研究

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, based on the information and data extracted from the magnetic resonance imaging(MRI) we will study the spontaneous oscillatons of the blood oxygenation level dependent signals in the human brain networks. We will investigate the spatiotemporal patterns of spontaneous oscillations, with the application of achievements in the previous theoretical study. Furhtermore the mechanism of both wave propagation and self-organization in the complex brain networks will aslo be explored. In conclusion，this project will make a further understanding of the microscopic mechanism of both macroscopic behavior and synergetic phenomena in complex systems. We hope our study will provide some insights into the intrinsic principle of the self-organization of the brain function.

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。

社会系统、生物系统等领域广泛存在复杂网络结构，脑网络就是一个典型的例子。已有研究表明大脑中神经活动的时空斑图与脑的信息处理紧密相关。研究复杂网络上自持续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运行机制有重要意义。本项目按申请计划，开展了以下两个方面的研究：一方面是关于可激发节点复杂网络上振荡斑图的理论研究，根据实际神经网络的拓扑特征，分别研究小世界网络和无标度网络上不同类型振荡行为的时空斑图和形成机制，并结合主相超前驱动方法，简化复杂的振荡斑图，识别同步发放的振荡源及波的传播路径；另一方面是人脑网络振荡行为的实证研究，我们结合已有的多模态磁共振影像数据，重构人脑功能和结构网络，考察了基于血氧水平依赖信号自发波动的人脑功能网络的时空斑图及其与底层白质纤维结构网络的拓扑关联。此外，我们还基于快速成像的磁共振影像数据，开展人脑功能网络和结构网络构建的计算模型研究，进一步丰富了原申请书的内容。以上研究拓展了复杂网络上的斑图动力学的研究，对于我们理解复杂系统中宏观组织行为的微观机制具有重要意义。在该项目的资助下，我们在复杂网络斑图动力学的理论分析和实证研究方面共发SCI论文7篇，培养年轻教师1名，项目组成员参加了国际人脑年会等国内外重要会议。