复杂网络上动力学系统同步现象的研究

发布时间：2018-04-21 09:43

本文选题：复杂网络 + 网络平均距离　；参考：《广西师范大学》2015年硕士论文

【摘要】：随着人们生活日益的网络化,复杂网络已经成为一个跨学科的新兴领域,吸引了大量学者对其进行研究。复杂网络是对现实生活中各种复杂系统的描述,是通过把系统中的个体简化为节点,个体间的相互关系用边的连接来表示的方法获得的。理解网络结构特征对网络动力学行为的影响,进而对网络行为进行预测和改善是研究复杂网络的主要目标之一,复杂网络上动力系统的同步是其中的一项重要研究内容,具有重要的科学研究意义和实际应用价值。在本论文,我们研究了网络距离对同步能力的影响,探讨了在群落网络中网络复杂度与单个群落的同步状态随群落间连边数量的变化情况,分析了网络距离与复杂度的关系,具体内容如下：(1)网络平均距离是重要的网络结构特征量,它对网络同步能力有着重要的影响。以集聚系数和度分布保持不变的规则网络模型为基础,通过数值模拟分析,我们发现无论网络同步区域是有界的还是半无界的,网络平均距离越小,网络的同步能力越强。同时,我们还考察了网络节点间距离分布的异质性对网络同步能力的影响,给出了它们不同的数值关系。(2)对群落网络中整个网络复杂度与单个群落同步状态进行了比较。通过改变群落间的连边数量,分别在三种不同的情况下考察单个群落的同步状态与网络复杂度的变化情况：不同的振子作为网络节点的动力学系统,不同的网络耦合强度,不同的网络平均度。通过数值模拟发现；网络复杂度的极大值与单个群落同步状态的极小值的位置非常接近,这表明在极值附近网络处于在保持网络整体信息通畅前提下实现的最大独立程度的位置。(3)生活中常见的同步现象一般是处于部分同步状态,鉴于复杂度是研究网络部分同步的重要参数,我们研究了网络平均距离对复杂度的影响。研究发现随着平均距离的增加,复杂度都是先增加后减小的,表明在这一过程中网络中先存在大的同步团簇,之后大同步团簇破裂成小的同步团簇,平均距离的继续增加导致小的同步团簇也破碎掉。
[Abstract]:With the increasing network of people's life, complex network has become an interdisciplinary emerging field, attracting a large number of scholars to study it. Complex network is a description of various complex systems in real life. It is obtained by simplifying the individual in the system into nodes, and the relationship between individuals is represented by edge connection. It is one of the main goals of studying complex networks to understand the influence of network structure characteristics on network dynamic behavior, and then to predict and improve network behavior. Synchronization of dynamic systems on complex networks is one of the important research contents. It has important scientific research significance and practical application value. In this paper, we study the influence of network distance on synchronization ability, discuss the change of network complexity and synchronization status of a single community with the number of connected edges in a community network, and analyze the relationship between network distance and complexity. The main contents are as follows: (1) the average distance of network is an important characteristic quantity of network structure, which has an important influence on the network synchronization ability. Based on the regular network model with invariant agglomeration coefficient and degree distribution, we find that no matter whether the network synchronization region is bounded or semi-unbounded, the smaller the average distance of the network is, the stronger the synchronization capability of the network is. At the same time, we also investigate the influence of the heterogeneity of the distance distribution between the nodes on the synchronization ability of the network, and give their different numerical relationships. The complexity of the whole network in the community network is compared with the synchronization state of a single community. By changing the number of connected edges between communities, the changes of synchronization state and network complexity of a single community are investigated under three different conditions: different oscillators act as dynamic systems of network nodes, and different network coupling intensities. Different network averages. Through numerical simulation, it is found that the maximum of network complexity is very close to the minimum value of the synchronization state of a single community. This indicates that the network near the extremum is in the position of the maximum degree of independence realized under the premise of keeping the whole network information unobstructed.) the common synchronization phenomenon in life is generally in the state of partial synchronization. Since complexity is an important parameter in studying network partial synchronization, we study the influence of network average distance on complexity. It is found that with the increase of the average distance, the complexity increases first and then decreases, which indicates that in this process there are first large synchronous clusters, and then the large synchronous clusters break down into small synchronous clusters. The increasing of the average distance leads to the breakup of the small synchronous clusters.
【学位授予单位】：广西师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5

【相似文献】