复杂网络上可激发振子的非线性动力学

发布时间：2018-07-20 20:53

【摘要】：我们都生活在网络的时代,现在网络已经扩展到一个很宽泛的领域,从反映人际交往的社交网络到演绎人类认知行为的神经网络等等。见证了研究许多自然和人工的复杂系统所取得的成果之后,科学家最近几年也开始将注意力转移到在复杂网络动力学上的宏观现象,复杂网络的研究也有了飞快地发展。但是先前的这些工作都强调了复杂网络拓扑结构对网络动力学研究的重要作用。然而,大家都很少把注意力放在局部动力学或者是网络局部对集体振荡动力学的影响方面,所有的模型都是研究复杂网络上突发的现象。因为可激发振子有各种比较现实的应用,像流行性疾病的传播、神经元网络等,所以研究可激发的振子具有很重要的意义。在本文中我们主要考虑的是可激发系统中,局部动力学和相互作用的网络振子是如何在复杂网络动力学中发挥至关重要作用的。本文的前三章主要介绍了所研究内容的背景和发展历史,包括复杂网络的发展历程和网络特征,动态系统的稳定性。在第四章中,我们研究了在有序的可激发网络当中的集体振荡现象。我们先是从理论上分析了初始状态的稳定性,发现有两种途径可以改变初始状态的稳定性：静态路径和振荡路径。我们发现者两种路径和所涉及到的分叉都与网络的拓扑结构是没有关系的。相反,它与局域动力学和振子之间的耦合方式有很大的关系。考虑到S耦合方式和D耦合方式是建立神经网络模型的候选耦合方式,我们在这篇文章中将使用这两种耦合方式。第五章为全文的总结与展望。总结了网络动力学行为与其最大本征值对应的本征矢之间的关系,并提出将来研究复杂网络将面对的困难。
[Abstract]:We all live in the era of the Internet, now the network has expanded to a very broad field, from the social network reflecting interpersonal communication to the neural network that deduces human cognitive behavior and so on. After witnessing the achievements of many natural and artificial complex systems, scientists have begun to shift their attention to the macroscopic phenomena in the dynamics of complex networks in recent years, and the study of complex networks has also developed rapidly. However, these previous studies have emphasized the important role of complex network topology in the study of network dynamics. However, little attention is paid to the local dynamics or the effect of the local network on the collective oscillation dynamics. All the models are concerned with the phenomenon of burst in complex networks. It is of great significance to study the excitable oscillator because of its various practical applications, such as epidemic disease transmission, neural network and so on. In this paper, we mainly consider how the local dynamics and the interacting network oscillator play an important role in the complex network dynamics. The first three chapters of this paper mainly introduce the background and history of the research, including the development of complex networks and network characteristics, the stability of dynamic systems. In the fourth chapter, we study the collective oscillation in an ordered excitable network. First we analyze the stability of the initial state theoretically and find that there are two ways to change the stability of the initial state: the static path and the oscillation path. The two paths of the discoverer and the bifurcation involved are not related to the topology of the network. On the contrary, it is closely related to the local dynamics and the mode of coupling between oscillators. Considering that S-coupling and D-coupling are candidates for neural network models, we will use them in this paper. The fifth chapter is the summary and prospect of the full text. The relationship between the dynamical behavior of the network and the eigenvector corresponding to its maximum eigenvalue is summarized, and the difficulties to study the complex network in the future are put forward.
【学位授予单位】：北京邮电大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

【共引文献】