本文關(guān)鍵詞：兩層復(fù)雜動力網(wǎng)絡(luò)的廣義外同步　出處：《武漢大學》2016年博士論文　論文類型：學位論文

  更多相關(guān)文章： 兩層網(wǎng)絡(luò) 輔助系統(tǒng)方法 牽制控制 廣義同步 度分布異質(zhì)性 同步能力

【摘要】：現(xiàn)實世界中存在的大量復(fù)雜系統(tǒng)都可以通過網(wǎng)絡(luò)來描述,比如萬維網(wǎng),電力網(wǎng)絡(luò),運輸網(wǎng)絡(luò),神經(jīng)網(wǎng)絡(luò),人際關(guān)系網(wǎng)等等.這些網(wǎng)絡(luò)盡管看上去各不相同,但是卻有越來越多的研究結(jié)果表明它們有著驚人的相似之處.自從發(fā)現(xiàn)大量的真實網(wǎng)絡(luò)具有小世界和無尺度的特征后,人們將節(jié)點動力學與復(fù)雜網(wǎng)絡(luò)的拓撲結(jié)構(gòu)結(jié)合起來考慮,提出復(fù)雜動力網(wǎng)絡(luò)模型,它是刻畫各種不同拓撲結(jié)構(gòu)和動力學性質(zhì)的一種有力工具.近年來,復(fù)雜網(wǎng)絡(luò)的群體行為得到了人們的廣泛關(guān)注,尤其是單個或多個復(fù)雜網(wǎng)絡(luò)的同步.同步是實際世界普遍存在的一種自然現(xiàn)象,比如鳥群的遷徙,魚群的游動,螢火蟲的同步閃爍等等,其研究越來越受到研究者的高度重視,也因此成為本論文的研究主題.本論文主要內(nèi)容分為五章,第一章簡要介紹了與后續(xù)章節(jié)相關(guān)的復(fù)雜網(wǎng)絡(luò)的基礎(chǔ)知識,并指出復(fù)雜動力網(wǎng)絡(luò)同步問題的研究現(xiàn)狀和本論文的研究背景.二至五章為正文部分,詳細介紹本論文的工作及創(chuàng)新點.第六章是在本論文的基礎(chǔ)上,給出我們對今后工作的展望.全文的主要內(nèi)容和創(chuàng)新成果有如下幾個方面：(1)在現(xiàn)實世界中的復(fù)雜網(wǎng)絡(luò)很多都存在著各種不確定的信息,比如節(jié)點動力學中未知的參數(shù).毫無疑問,參數(shù)未知情況下的復(fù)雜動力網(wǎng)絡(luò)的研究是一個傳統(tǒng)并具有挑戰(zhàn)性的問題.在第二章中研究了節(jié)點動力學中參數(shù)未知、函數(shù)關(guān)系未知的、網(wǎng)絡(luò)拓撲結(jié)構(gòu)也不同的更一般的復(fù)雜動力網(wǎng)絡(luò)的廣義外同步.即當驅(qū)動網(wǎng)絡(luò)的節(jié)點狀態(tài)與其在響應(yīng)網(wǎng)絡(luò)中的對應(yīng)節(jié)點的狀態(tài)滿足某種已知的函數(shù)關(guān)系時,給出了在這種情況下的兩個不同復(fù)雜動力網(wǎng)絡(luò)達到廣義外同步的充分條件.但在現(xiàn)實網(wǎng)絡(luò)中,這種函數(shù)關(guān)系往往是未知的,因此在第三章研究了函數(shù)關(guān)系未知的復(fù)雜網(wǎng)絡(luò)的廣義外同步,給出了基于輔助系統(tǒng)方法的參數(shù)未知的兩個不同復(fù)雜網(wǎng)絡(luò)達到廣義外同步的一個充分條件.(2)復(fù)雜網(wǎng)絡(luò)的牽制控制是以控制局部來達到影響整個網(wǎng)絡(luò)的群體行為.通過對單層網(wǎng)絡(luò)牽制控制的分析,我們研究了具有單向耦合的兩層網(wǎng)絡(luò)的牽制廣義同步.在第四章中,我們提出了基于驅(qū)動的具有層間單向耦合的兩層網(wǎng)絡(luò)達到廣義同步的牽制控制策略,給出了基于輔助系統(tǒng)方法的兩層網(wǎng)絡(luò)達到牽制廣義同步的充分條件,發(fā)現(xiàn)了在所給的參數(shù)值和控制條件下,兩層網(wǎng)絡(luò)的對應(yīng)節(jié)點之間存在一定的函數(shù)關(guān)系,只不過這種關(guān)系是未知的,即驗證了層間廣義同步的存在.同時也發(fā)現(xiàn)了兩層網(wǎng)絡(luò)達到廣義同步所需要牽制節(jié)點的個數(shù)依賴于響應(yīng)層網(wǎng)絡(luò)的密度,即隨著響應(yīng)層網(wǎng)絡(luò)的邊越稠密所需牽制的節(jié)點數(shù)越少；隨著響應(yīng)層層內(nèi)耦合強度的增加,牽制的節(jié)點數(shù)目減少.(3)對節(jié)點數(shù)相同的兩層網(wǎng)絡(luò)而言,當一層網(wǎng)絡(luò)中的每一個節(jié)點與另一層網(wǎng)絡(luò)的一個節(jié)點連接時,可以是兩個單層的度大的節(jié)點與度大的節(jié)點連接,度小的節(jié)點與度小的節(jié)點連接；或是一層網(wǎng)絡(luò)度大的節(jié)點與另一層度小的節(jié)點連接；或是一層網(wǎng)絡(luò)的節(jié)點與另一層網(wǎng)絡(luò)的節(jié)點隨機連接.因此,基于這樣的想法,在第四章中,我們討論了具有層間單向耦合的兩層網(wǎng)絡(luò)在這三種不同的連接狀態(tài)下的牽制策略,給出了在三種不同的牽制策略下,兩層網(wǎng)絡(luò)達到廣義同步所需要牽制的節(jié)點的個數(shù)與響應(yīng)層網(wǎng)絡(luò)的層內(nèi)耦合強度有關(guān),即當驅(qū)動層層內(nèi)耦合強度比較大時,牽制度大節(jié)點的數(shù)目少；而當驅(qū)動層層內(nèi)耦合強度比較小時,牽制度小節(jié)點的數(shù)目少。因此,當驅(qū)動層網(wǎng)絡(luò)層內(nèi)耦合強度從小到大變化時,需要選擇不同的牽制策略.(4)現(xiàn)實中,絕大多數(shù)復(fù)雜系統(tǒng)的節(jié)點具有多種功能,并且相互連接和作用,而這多種功能之間有質(zhì)的區(qū)別,不能疊加,從而構(gòu)成了多層網(wǎng)絡(luò).多層網(wǎng)絡(luò)已成為復(fù)雜網(wǎng)絡(luò)科學研究的前沿問題之一,而其中一個重要的問題就是多層網(wǎng)絡(luò)的同步能力研究.在第五章中,研究了在同步區(qū)域無界和有界兩種情況下,更一般的度分布可調(diào)的兩層網(wǎng)絡(luò)的同步能力,分別討論了兩層網(wǎng)絡(luò)度分布異質(zhì)性同時改變或一層網(wǎng)絡(luò)異質(zhì)性改變,一層網(wǎng)絡(luò)異質(zhì)性固定時,兩層網(wǎng)絡(luò)的異質(zhì)性,層間、層內(nèi)耦合強度對網(wǎng)絡(luò)同步能力的影響.
[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.

【學位授予單位】：武漢大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O157.5

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