本文關(guān)鍵詞：復(fù)雜系統(tǒng)中的資源配置與演化動(dòng)力學(xué)研究　出處：《蘭州大學(xué)》2016年博士論文　論文類(lèi)型：學(xué)位論文

  更多相關(guān)文章： 復(fù)雜系統(tǒng) 統(tǒng)計(jì)物理 非線(xiàn)性動(dòng)力學(xué) 少數(shù)者博弈 資源配置 自組織 涌現(xiàn) 控制

【摘要】：真實(shí)復(fù)雜系統(tǒng)中普遍存在著大量個(gè)體競(jìng)爭(zhēng)有限資源的情形,豐富的宏觀現(xiàn)象得以涌現(xiàn),如羊群行為、恐慌、踩踏事件、公共地悲劇、股價(jià)失控等,我們研究這些宏觀現(xiàn)象涌現(xiàn)的微觀機(jī)制,為復(fù)雜系統(tǒng)的優(yōu)化與控制提供啟發(fā)。有效的資源配置有助于提高系統(tǒng)資源利用率,因而如何通過(guò)不同的控制方式優(yōu)化系統(tǒng)的資源配置就是一個(gè)具有重要理論和現(xiàn)實(shí)意義的問(wèn)題,引起了復(fù)雜系統(tǒng)領(lǐng)域研究者的廣泛興趣,基于實(shí)驗(yàn)觀察和對(duì)真實(shí)系統(tǒng)的數(shù)據(jù)分析,相應(yīng)的模型和理論體系得以建立�；诖�,人們對(duì)不同背景下的的資源配置進(jìn)行了研究并取得了一些有意義的結(jié)果,并且這些結(jié)果對(duì)非平衡統(tǒng)計(jì)力學(xué)的理解有進(jìn)一步的促進(jìn)作用。我們針對(duì)復(fù)雜系統(tǒng)的資源配置過(guò)程展開(kāi)研究,發(fā)現(xiàn)了分組涌現(xiàn)現(xiàn)象,此外,針對(duì)羊群行為造成的資源利用率低下的現(xiàn)象,提出了釘扎控制的方法并建立了理論框架。觀點(diǎn)的傳遞以及觀點(diǎn)對(duì)個(gè)體行為的影響是復(fù)雜系統(tǒng)與復(fù)雜網(wǎng)絡(luò)領(lǐng)域研究的另一個(gè)焦點(diǎn)。例如,在最近十幾年中,研究者們常將演化博弈與觀點(diǎn)傳播進(jìn)行結(jié)合性研究,繼而探索個(gè)體之間的相互作用方式如何影響系統(tǒng)的動(dòng)力學(xué)行為。通過(guò)將演化博弈和觀點(diǎn)傳播進(jìn)行融合,我們建立了一個(gè)超對(duì)策博弈模型,并對(duì)社會(huì)系統(tǒng)中觀點(diǎn)傳播對(duì)合作涌現(xiàn)的影響做了嘗試性解釋。本論文的具體框架和研究創(chuàng)新點(diǎn)如下:在第一章,我們首先對(duì)刻畫(huà)復(fù)雜網(wǎng)絡(luò)性質(zhì)的統(tǒng)計(jì)學(xué)參量以及常見(jiàn)的網(wǎng)絡(luò)模型進(jìn)行了簡(jiǎn)要介紹。隨后對(duì)資源配置中兩個(gè)常見(jiàn)模型(少數(shù)者博弈和布爾博弈)以及演化博弈動(dòng)力學(xué)的相關(guān)理論(納什均衡、演化穩(wěn)定策略、復(fù)制動(dòng)態(tài)方程等)進(jìn)行了較為詳盡的闡述。最后,我們對(duì)復(fù)雜網(wǎng)絡(luò)以及復(fù)雜系統(tǒng)中常用的數(shù)學(xué)方法和理論做了介紹,包含平均場(chǎng)理論、馬爾科夫過(guò)程、主方程、生成函數(shù)等。在第二章,我們基于少數(shù)者獲勝的原則以及從眾的行為機(jī)制,建立了一個(gè)描述個(gè)體競(jìng)爭(zhēng)多個(gè)資源的少數(shù)者博弈模型。通過(guò)對(duì)模型的研究,我們發(fā)現(xiàn)多種資源根據(jù)其使用率的變化特征自發(fā)地分組,并顯現(xiàn)出震蕩行為。這些結(jié)果顯示系統(tǒng)低效率的潛在原因是資源的分組震蕩。此外,我們提出了描述該過(guò)程的數(shù)學(xué)框架,包括基于不考慮拓?fù)浣Y(jié)構(gòu)的平均場(chǎng)描述,以及考慮了個(gè)體間連接稀疏性的修正平均場(chǎng)描述,分別得到了與模擬相吻合的解析結(jié)果。此外,我們?cè)诠墒兄幸灿^察到了個(gè)股收益分組震蕩的現(xiàn)象,并對(duì)真實(shí)系統(tǒng)中大量出現(xiàn)的類(lèi)似行為做了討論。該工作所建立的理論將有助于真實(shí)社會(huì)系統(tǒng)中的資源競(jìng)爭(zhēng)、優(yōu)化分配等問(wèn)題的研究。在第三章,我們提出并建立了一種很直觀的控制方法——釘扎控制,用以控制個(gè)體基于可得到的信息選擇利用率低的資源引發(fā)的羊群行為。該行為常常導(dǎo)致大多數(shù)個(gè)體擁擠并競(jìng)爭(zhēng)個(gè)別的資源而其他資源空閑的結(jié)果。釘扎控制的方法能夠非常有效地抑制資源分配動(dòng)力學(xué)過(guò)程中的羊群行為。我們發(fā)現(xiàn)僅僅通過(guò)固定(釘扎)很少數(shù)個(gè)體對(duì)資源的選擇性,而保留大多數(shù)個(gè)體能夠自由選擇資源,就能夠消除羊群行為。我們系統(tǒng)地研究了隨機(jī)釘扎和傾向性釘扎等釘扎策略、全連接圖和無(wú)標(biāo)度網(wǎng)絡(luò)等個(gè)體相互作用網(wǎng)絡(luò)結(jié)構(gòu)下的釘扎控制過(guò)程,并且提出了基于平均場(chǎng)理論框架下的完全的解析理論來(lái)幫助理解控制的實(shí)現(xiàn)機(jī)制。在第四章,我們針對(duì)不同釘扎模式下釘扎調(diào)控是否有助于資源配置的優(yōu)化進(jìn)行了更為廣泛的探討。在研究中,我們發(fā)現(xiàn)對(duì)于給定的具有一定異質(zhì)性的網(wǎng)絡(luò)中,在異化的相互作用方式下,存在一個(gè)獨(dú)立于釘扎模式的最優(yōu)釘扎密度。在該釘扎密度下,系統(tǒng)的資源配置得到了最大程度的優(yōu)化。隨后,我們發(fā)展了一套理論用以解釋最優(yōu)釘扎密度的涌現(xiàn),并預(yù)測(cè)了最優(yōu)釘扎密度對(duì)網(wǎng)絡(luò)拓?fù)浣Y(jié)構(gòu)的依賴(lài)關(guān)系。這些工作為存在少數(shù)者博弈機(jī)制的復(fù)雜動(dòng)力系統(tǒng)中漲落等問(wèn)題的研究提供給了一個(gè)基本的、普遍的框架,這對(duì)社會(huì)、生態(tài)以及政治體系中相關(guān)問(wèn)題的研究有重要的啟發(fā)和潛在的應(yīng)用價(jià)值。在第五章,鑒于社會(huì)系統(tǒng)中合作往往以混合策略的形式出現(xiàn),我們將經(jīng)典的囚徒困境博弈與觀點(diǎn)博弈相結(jié)合構(gòu)造了一個(gè)超對(duì)策博弈的演化動(dòng)力學(xué)模型,該模型中個(gè)體的決策由自身對(duì)博弈的觀點(diǎn)決定。通過(guò)數(shù)值模擬,系統(tǒng)出現(xiàn)了以混合策略形式涌現(xiàn)的合作現(xiàn)象,此外,我們根據(jù)模擬的部分結(jié)果給出了以混合策略形式出現(xiàn)的高合作比例所需的條件進(jìn)而分析出不同參數(shù)對(duì)該條件的影響。通過(guò)對(duì)參數(shù)的分析,可得知較溫和的社會(huì)環(huán)境、個(gè)體對(duì)虛假信息的較強(qiáng)警惕性能促進(jìn)高合作比例的混合策略的涌現(xiàn)。這些結(jié)果有利于促進(jìn)我們對(duì)真實(shí)社會(huì)系統(tǒng)個(gè)體之間相互作用形式的理解,具有一定現(xiàn)實(shí)意義。在第六章,我們對(duì)已有的工作進(jìn)行了總結(jié),并對(duì)未來(lái)的研究方向和研究思路進(jìn)行了展望。
[Abstract]:The real complex system exists in a large number of individual competition for limited resources, rich macroscopic phenomenon has emerged, such as herd behavior, panic and stampede tragedy of public land, the price is out of control, we study the microscopic mechanism of the emergence of these phenomena, to provide inspiration for the optimization and control of complex system. Effective resource allocation help to improve the utilization rate of system resources, so how to control the different ways of optimizing the system of resource allocation is one of the important theoretical and practical significance of the problem, has aroused wide interest in the field of complex system research, analysis and experimental observation on real system based on the data, to be able to establish the corresponding model and based on the theoretical system. This, people of different backgrounds of the allocation of resources is studied and some significant results were obtained, and the results of non equilibrium statistical mechanics Understanding a further role. We studied for complex system resource allocation process, found the packet emerging phenomenon, in addition, the low utilization rate of resources resulting in herd behavior phenomenon, put forward the control method with nail and set up a theoretical framework. Another focus view influence point and point of view of transfer the behavior of the individual is the study of complex systems and complex networks field. For example, in recent years, researchers used evolutionary game theory and ideas combined with research, and to explore how the interaction between individuals of the dynamic behavior of the system. Through combination of evolutionary game and views, we establish a super game model, and the point of view of the social system of communication cooperation makes a tentative explanation. The specific framework and research innovation such as : in the first chapter, we firstly describe the statistical parameters of complex networks and the common network model was briefly introduced. Then the allocation of resources in the two common model (minority game and Boolean game) and the related theory of evolutionary game dynamics (Nash equilibrium, evolutionary stable strategy, replicated dynamic equation) of a more detailed exposition. At last, we introduced the theory and method of mathematics used in complex systems and complex networks, including the mean field theory, Markov process, master equation, generating function and so on. In the second chapter, we based on a few wins and the principle of conformity behavior mechanism, establishes a game model of minorities. A description of the individual competition more resources. Through the research of the model, we found a variety of resources according to its variation rate of spontaneous grouping and showing concussion Behavior. These results indicate that the potential causes of the low efficiency of the system is the packet shock resources. In addition, we propose a mathematical description framework of the process, including not considering the mean field description based on topological structure, and consider the connection between individuals modified sparsity mean field description, are obtained. The analytical results are consistent with the simulation in the stock market. In addition, we also observed the stock return packet shock phenomenon, similar behavior and the emergence of a large number of real systems is discussed. The establishment of the work of the theory will help real social system resource competition, research on the optimization of the allocation problem. In the third chapter, we put forward and the establishment of a direct control method of pinning control, used to control the herding behavior of individual based on information available to the selection of low utilization rate of resources caused by the behavior often leads to most. The individual competition of individual resources crowded and other resources idle control method. The nail bar can effectively inhibit the herd behavior in the process of dynamic resource allocation. We found that only through a fixed (pinning) very few individuals of resources and selectivity, to retain a large majority of individuals to choose resources, you can eliminate the sheep behavior. We systematically studied the random pinning and orientation pinning pinning strategy, fully connected graph and non pinning control process of scale-free networks and individual interaction network structure, and puts forward the analysis based on the theory of complete mean field theory to help understand the mechanism of control. In the fourth chapter, we focused on the different pinning mode optimization with nail will help control the allocation of resources for a more extensive discussion. In this study, we found that for a given out there A heterogeneous network, in the interaction of alienation, there is an optimal pinning model independent of pinning density. The pinning density, system resource configuration has been optimized to the maximum extent. Then, we develop a theory to explain the emergence of optimal pinning density, and to predict the optimal pinning density dependence of the topological structure of the network. To provide research work for the fluctuations of these complex dynamical systems exist game mechanism minority issues in a basic, general framework, this research on social issues related to ecological and political system has an important inspiration and the potential application value. In the fifth chapter, in view of the social system of cooperation often appears in the mixed strategy, we will view the prisoner's dilemma game and game classic combination structure of a super dynamic evolution game The mechanical model, the model of individual decision making in the game is decided by its own point of view. Through numerical simulation, the emergence of cooperative phenomena, to form a mixed strategy system emerged in addition, according to the simulated results are given in the form of a high proportion of mixed strategy cooperation conditions required for the further analysis of the influence of different parameters on the condition. Through the analysis of parameters, the more moderate social environment, strong vigilance performance of individual false information to promote the high proportion of the mixed strategy cooperation emerge. These results are helpful for promoting our understanding of the interaction between the real form of the social system of the individual, has a certain practical significance. In the sixth chapter, we the work is summarized and the future research direction and research ideas are discussed.

【學(xué)位授予單位】：蘭州大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：N941.4
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本文編號(hào)：1374554