本文選題：指數(shù)同步 + QUAD條件�。� 參考：《武漢大學》2017年博士論文

【摘要】：在人類社會生活中,隨著社會信息化的高速發(fā)展,復雜網(wǎng)絡(luò)與我們的生活息息相關(guān),復雜網(wǎng)絡(luò)的研究不僅具有深刻的理論意義也具有廣泛的實際應(yīng)用價值.復雜網(wǎng)絡(luò)的動力學行為是網(wǎng)絡(luò)科學中重要的研究內(nèi)容,它是網(wǎng)絡(luò)的拓撲結(jié)構(gòu)和微分方程相互交叉的研究領(lǐng)域,因此具有重要的理論意義和應(yīng)用價值.同步和一致做為復雜網(wǎng)絡(luò)中最典型的動力學現(xiàn)象,同步和一致在眾多的學科領(lǐng)域以及工程應(yīng)用中都具有廣泛的應(yīng)用前景.在復雜網(wǎng)絡(luò)的同步和一致性研究中,為了研究的方便,研究者往往會對個體的動力學以及網(wǎng)絡(luò)拓撲結(jié)構(gòu)給予各種假設(shè),而實際中的復雜網(wǎng)絡(luò)系統(tǒng)中的個體的動力學以及網(wǎng)絡(luò)拓撲結(jié)構(gòu)卻復雜得多,復雜網(wǎng)絡(luò)的同步和一致研究中還有很多待解決的問題.在前人的研究基礎(chǔ)上,利用圖論、矩陣理論以及動力系統(tǒng)理論,本文進一步研究了復雜網(wǎng)絡(luò)中的同步和一致性問題,其中在同步研究的部分,本文改進了個體動力學的假設(shè)條件,在一致性的研究部分,一方面考慮網(wǎng)絡(luò)拓撲結(jié)構(gòu)更復雜的系統(tǒng),另一方面考慮個體動力學方程為分數(shù)階的系統(tǒng).具體的,本文一共分為六章,其中第一,二章簡要的敘述了復雜網(wǎng)絡(luò)的同步及一致性的研究背景和現(xiàn)狀,以及介紹了一些與研究內(nèi)容相關(guān)的預(yù)備知識,第三到五章為本文的研究工作,最后,在第六章對本文的研究內(nèi)容進行總結(jié)并對未來的研究工作進行展望.本文的主要研究內(nèi)容如下.1.在第三章中研究了個體自身的非線性動力學不需要滿足QUAD條件或者弱的QUAD條件的線性耦合動力系統(tǒng)的指數(shù)同步問題,提出了兩類更弱的動力學條件,給出此時關(guān)于系統(tǒng)實現(xiàn)同步的定理及推論,并在數(shù)值仿真中將本文的同步理論用于Hopfield神經(jīng)網(wǎng)絡(luò),說明了本文理論的有效性和正確性.2.在第四章中給出了具有連續(xù)時間動態(tài)改變的拓撲結(jié)構(gòu)的多智能體系統(tǒng)的有限時間協(xié)議,其中為了簡化研究我們只考慮拓撲是無向的情況,應(yīng)用圖論、有限時間穩(wěn)定理論,得到了系統(tǒng)實現(xiàn)局部有限時間一致和全局有限時間一致的條件,接下來也對系統(tǒng)實現(xiàn)有限時間一致的最短時間進行了估計,給出其滿足的不等式條件,此外,我們也理論的證明了本章所給的有限時間一致性協(xié)議同樣也適用于多智能體系統(tǒng)拓撲結(jié)構(gòu)為固定或切換時的情況,最后數(shù)值仿真的實例也說明了這些結(jié)論的正確性.3.隨著分數(shù)階微積分的發(fā)展,許多自然界中的現(xiàn)象用具有分數(shù)階動力學行為的系統(tǒng)可以得到很好的解釋,同時在許多工程系統(tǒng)中,與整數(shù)階模型相比,分數(shù)階微分模型往往能更準確地模擬系統(tǒng)動力學過程,因此本文在第五章中研究了具有有向拓撲結(jié)構(gòu)的分數(shù)階多智能體系統(tǒng)在非線性協(xié)議下的一致問題,應(yīng)用圖論、矩陣理論和分數(shù)階微積分的性質(zhì),給出非線性協(xié)議下分數(shù)階多智能體實現(xiàn)一致的條件并給出了文中系統(tǒng)的一致值的具體表達式,同時給出具體的仿真實例,說明了分數(shù)階多智能體在非線性協(xié)議下的一些特征,并與現(xiàn)有線性協(xié)議的結(jié)果進行比較.
[Abstract]:In human social life, with the rapid development of social information, complex networks are closely related to our lives. The study of complex networks not only has profound theoretical significance but also has extensive practical application value. The dynamic behavior of complex networks is the important research content of network science, it is the topology structure and micro network of network. It has important theoretical significance and application value. Synchronization and consistency are the most typical dynamic phenomena in complex networks. Synchronization and consistency have wide application prospects in many subject fields and engineering applications. In the study of synchronization and consistency of complex networks, for research It is convenient for researchers to give various assumptions about the dynamics of individual and network topology, and the dynamics of individual and network topology in the complex network system are much more complex. There are many problems to be solved in the synchronization and consistent research of complex networks. Based on previous studies, the graph theory is used. The problem of synchronization and consistency in complex networks is further studied by matrix theory and dynamic system theory. In the part of synchronization research, this paper improves the hypothesis of individual dynamics, in the research part of consistency, on the one hand, considering the more complex system of network topology, and on the other hand, the individual dynamics side is considered. This paper is divided into six chapters. In this paper, this paper is divided into six chapters. The first, second chapters briefly describe the background and status of the research on the synchronization and consistency of the complex network, and introduce some preparatory knowledge related to the research content. The third to five chapters are the research work of this paper. Finally, in the sixth chapter, the research content of this paper is introduced. The main research contents of this paper are as follows: in the third chapter,.1. studies the exponential synchronization problem of linear coupled dynamic systems that do not have to satisfy the QUAD condition or weak QUAD condition in the nonlinear dynamics of individual itself. The two kinds of weaker dynamic conditions are proposed, and the system is given at this time. The theorem and inference of synchronization are realized, and the synchronization theory of this paper is applied to the Hopfield neural network in numerical simulation, and the validity and correctness of this theory is illustrated by.2.. In the fourth chapter, the limited time protocol of a multi-agent system with a continuous time dynamic topology is given. In order to simplify the study we only Considering the fact that topology is undirected, using graph theory and finite time stability theory, the conditions for the system to achieve local finite time consistency and global finite time consistency are obtained. Then, the shortest time time consistency of the system is estimated, and the inequality conditions are given. In addition, we also prove this theory. The finite time conformance protocol given by the chapter also applies to the condition that the topology of the multi-agent system is fixed or switched. Finally, the example of numerical simulation also shows the correctness of these conclusions.3., with the development of fractional calculus, many natural phenomena which have fractional order dynamic behavior can be obtained. It is well explained that in many engineering systems, compared with the integer order model, the fractional order differential model can more accurately simulate the dynamic process of the system. Therefore, in the fifth chapter, the uniform problem of the fractional order multi-agent system with a directional topology is discussed, the application graph theory, the matrix theory and the theory of the matrix are applied. The properties of fractional calculus are given, the conditions for achieving the consistency of the fractional order multiagent under the nonlinear protocol are given and the concrete expression of the uniform value of the system is given. At the same time, a specific simulation example is given, and some characteristics of the fractional order multi-agent under the nonlinear protocol are illustrated, and the results are compared with the results of the existing linear protocols.

【學位授予單位】：武漢大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：O157.5

【參考文獻】

相關(guān)期刊論文 前4條

1 石霞;張佳棟;;Interaction function of coupled bursting neurons[J];Chinese Physics B;2016年06期

2 楊科利;;耦合不連續(xù)系統(tǒng)同步轉(zhuǎn)換過程中的多吸引子共存[J];物理學報;2016年10期

3 吳大宇;趙艷萍;鄭木華;周杰;劉宗華;;Reverse-feeding effect of epidemic by propagators in two-layered networks[J];Chinese Physics B;2016年02期

4 ;DISTRIBUTED FINITE-TIME χ-CONSENSUS ALGORITHMS FOR MULTI-AGENT SYSTEMS WITH VARIABLE COUPLING TOPOLOGY[J];Journal of Systems Science & Complexity;2010年02期

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本文編號：1819946