两层复杂动力网络的广义外同步

发布时间：2018-01-02 13:14

本文关键词：两层复杂动力网络的广义外同步　出处：《武汉大学》2016年博士论文　论文类型：学位论文

【摘要】：现实世界中存在的大量复杂系统都可以通过网络来描述,比如万维网,电力网络,运输网络,神经网络,人际关系网等等.这些网络尽管看上去各不相同,但是却有越来越多的研究结果表明它们有着惊人的相似之处.自从发现大量的真实网络具有小世界和无尺度的特征后,人们将节点动力学与复杂网络的拓扑结构结合起来考虑,提出复杂动力网络模型,它是刻画各种不同拓扑结构和动力学性质的一种有力工具.近年来,复杂网络的群体行为得到了人们的广泛关注,尤其是单个或多个复杂网络的同步.同步是实际世界普遍存在的一种自然现象,比如鸟群的迁徙,鱼群的游动,萤火虫的同步闪烁等等,其研究越来越受到研究者的高度重视,也因此成为本论文的研究主题.本论文主要内容分为五章,第一章简要介绍了与后续章节相关的复杂网络的基础知识,并指出复杂动力网络同步问题的研究现状和本论文的研究背景.二至五章为正文部分,详细介绍本论文的工作及创新点.第六章是在本论文的基础上,给出我们对今后工作的展望.全文的主要内容和创新成果有如下几个方面：(1)在现实世界中的复杂网络很多都存在着各种不确定的信息,比如节点动力学中未知的参数.毫无疑问,参数未知情况下的复杂动力网络的研究是一个传统并具有挑战性的问题.在第二章中研究了节点动力学中参数未知、函数关系未知的、网络拓扑结构也不同的更一般的复杂动力网络的广义外同步.即当驱动网络的节点状态与其在响应网络中的对应节点的状态满足某种已知的函数关系时,给出了在这种情况下的两个不同复杂动力网络达到广义外同步的充分条件.但在现实网络中,这种函数关系往往是未知的,因此在第三章研究了函数关系未知的复杂网络的广义外同步,给出了基于辅助系统方法的参数未知的两个不同复杂网络达到广义外同步的一个充分条件.(2)复杂网络的牵制控制是以控制局部来达到影响整个网络的群体行为.通过对单层网络牵制控制的分析,我们研究了具有单向耦合的两层网络的牵制广义同步.在第四章中,我们提出了基于驱动的具有层间单向耦合的两层网络达到广义同步的牵制控制策略,给出了基于辅助系统方法的两层网络达到牵制广义同步的充分条件,发现了在所给的参数值和控制条件下,两层网络的对应节点之间存在一定的函数关系,只不过这种关系是未知的,即验证了层间广义同步的存在.同时也发现了两层网络达到广义同步所需要牵制节点的个数依赖于响应层网络的密度,即随着响应层网络的边越稠密所需牵制的节点数越少；随着响应层层内耦合强度的增加,牵制的节点数目减少.(3)对节点数相同的两层网络而言,当一层网络中的每一个节点与另一层网络的一个节点连接时,可以是两个单层的度大的节点与度大的节点连接,度小的节点与度小的节点连接；或是一层网络度大的节点与另一层度小的节点连接；或是一层网络的节点与另一层网络的节点随机连接.因此,基于这样的想法,在第四章中,我们讨论了具有层间单向耦合的两层网络在这三种不同的连接状态下的牵制策略,给出了在三种不同的牵制策略下,两层网络达到广义同步所需要牵制的节点的个数与响应层网络的层内耦合强度有关,即当驱动层层内耦合强度比较大时,牵制度大节点的数目少；而当驱动层层内耦合强度比较小时,牵制度小节点的数目少。因此,当驱动层网络层内耦合强度从小到大变化时,需要选择不同的牵制策略.(4)现实中,绝大多数复杂系统的节点具有多种功能,并且相互连接和作用,而这多种功能之间有质的区别,不能叠加,从而构成了多层网络.多层网络已成为复杂网络科学研究的前沿问题之一,而其中一个重要的问题就是多层网络的同步能力研究.在第五章中,研究了在同步区域无界和有界两种情况下,更一般的度分布可调的两层网络的同步能力,分别讨论了两层网络度分布异质性同时改变或一层网络异质性改变,一层网络异质性固定时,两层网络的异质性,层间、层内耦合强度对网络同步能力的影响.
[Abstract]:There are many complex systems in the real world can be described by the network, such as the world wide web, power network, transportation network, neural network, interpersonal relationship network and so on. These networks although it looks different, but there are more and more studies showed that they have striking similarities. Since the discovery of a large number of real network with the small world and scale-free features, people will topology dynamics and complex networks considering complex dynamical network model is proposed, which is a powerful tool to describe various topological structure and dynamic mechanical properties. In recent years, the group behavior of complex networks has been widely concerned, especially synchronous single or multiple complex networks. Synchronization is a widespread natural phenomenon in the real world, such as migratory birds, fish swimming, synchronized the fireflies Flash and so on, it has been paid more and more attention of researchers, has become the theme of this thesis. The main contents of this paper is divided into five chapters, the first chapter briefly introduces the basic knowledge of complex network and the following chapters, and points out the research status quo of synchronization of complex dynamical networks and the research background two. To the five chapter is the main body part, introduces the work and innovation of this paper. The sixth chapter is based on this paper, we give the outlook on the future work. The main contents and innovative achievements of the thesis are as follows: (1) complex networks in the real world there is a lot of variety uncertain information, such as the unknown node dynamics parameters. There is no doubt that the research of complex dynamical networks with unknown parameters under the condition of a traditional and challenging problem. In the second chapter of the Institute of research The parameters of the unknown node dynamics, unknown function, generalized external network topology is different and more general synchronization of complex dynamical networks. When the node state and in response to the corresponding drive network nodes in the network to meet the functional relationship some known, given two different complex dynamical networks to generalized abroad a sufficient condition for synchronization in this case. But in real networks, this function is often unknown, and generalized in the third chapter studies the relationship of the unknown function of complex network synchronization, given the unknown parameters of the auxiliary system approach in two different complex networks to achieve generalized synchronization of a sufficient condition. (2) based on pinning control of complex network with local control to achieve the effect of group behavior of the whole network. Through the analysis of the single-layer network pinning control, we study The two layer network with unidirectional coupling contain generalized synchronization. In the fourth chapter, we propose a drive layer between the one-way coupling two layer network to achieve generalized synchronization pinning control strategy based on two layer network auxiliary system method to contain sufficient conditions for generalized synchronization are given based on the parameters found in the to the value and control conditions, there is a certain relation between the corresponding nodes of two layer network, but this relationship is unknown, which validates the existence of generalized synchronization between layers. At the same time also found a number of two layer network to achieve broad synchronization node need to contain a response dependent on the density of the network layer that is, with the number of nodes in the network edges more dense layer response required to contain less; with the increase of the coupling strength of inner layer response, the number of nodes that contain less. (3) the same number of nodes and two layer network Say, when a layer of a node in the network each node and another layer of network connection, can be of two single node connected with the node degree is large, low degree nodes connected with the node degree is small; or a layer of large network node is connected with the other a layer of small nodes; or random node connecting node of the network layer and another layer of the network. Therefore, based on this idea, in the fourth chapter, we discuss the unidirectional coupling with inter layer two layer network in the three different connection conditions are given in the containment strategy. Three different containment strategy, the number of nodes in the two layer network to achieve generalized synchronization to contain related response coupling strength layer network layer, namely when the drive coupling strength of inner layer is large, the number of nodes less traction system; and when the coupling strength of inner layer is smaller than the drive When the number of nodes holding system less. Therefore, when the drive coupling strength varies from small to large in the network layer, the need to choose a different containment strategy. (4) in reality, the vast majority of nodes in complex systems with a variety of functions, and connected with each other and the role of a qualitative difference, between the various functions can to form a multilayer overlay network. Multilayer network has become one of the frontier research of complex network science, in which synchronization is an important problem of multi layer network. In the fifth chapter, the research in the synchronization region unbounded and bounded two case, two layer network synchronization capability degree distribution the general adjustable, respectively discusses the two layer network heterogeneous distribution of degree and change or a layer of network heterogeneity, a layer of fixed network heterogeneity, the heterogeneity, the two layer network layer, layer of network coupling strength The influence of the collaterals synchronization ability.

【学位授予单位】：武汉大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O157.5

【相似文献】