复杂系统中的资源配置与演化动力学研究

发布时间：2018-01-03 15:43

  本文关键词：复杂系统中的资源配置与演化动力学研究　出处：《兰州大学》2016年博士论文　论文类型：学位论文

  更多相关文章： 复杂系统 统计物理 非线性动力学 少数者博弈 资源配置 自组织 涌现 控制

【摘要】：真实复杂系统中普遍存在着大量个体竞争有限资源的情形,丰富的宏观现象得以涌现,如羊群行为、恐慌、踩踏事件、公共地悲剧、股价失控等,我们研究这些宏观现象涌现的微观机制,为复杂系统的优化与控制提供启发。有效的资源配置有助于提高系统资源利用率,因而如何通过不同的控制方式优化系统的资源配置就是一个具有重要理论和现实意义的问题,引起了复杂系统领域研究者的广泛兴趣,基于实验观察和对真实系统的数据分析,相应的模型和理论体系得以建立。基于此,人们对不同背景下的的资源配置进行了研究并取得了一些有意义的结果,并且这些结果对非平衡统计力学的理解有进一步的促进作用。我们针对复杂系统的资源配置过程展开研究,发现了分组涌现现象,此外,针对羊群行为造成的资源利用率低下的现象,提出了钉扎控制的方法并建立了理论框架。观点的传递以及观点对个体行为的影响是复杂系统与复杂网络领域研究的另一个焦点。例如,在最近十几年中,研究者们常将演化博弈与观点传播进行结合性研究,继而探索个体之间的相互作用方式如何影响系统的动力学行为。通过将演化博弈和观点传播进行融合,我们建立了一个超对策博弈模型,并对社会系统中观点传播对合作涌现的影响做了尝试性解释。本论文的具体框架和研究创新点如下:在第一章,我们首先对刻画复杂网络性质的统计学参量以及常见的网络模型进行了简要介绍。随后对资源配置中两个常见模型(少数者博弈和布尔博弈)以及演化博弈动力学的相关理论(纳什均衡、演化稳定策略、复制动态方程等)进行了较为详尽的阐述。最后,我们对复杂网络以及复杂系统中常用的数学方法和理论做了介绍,包含平均场理论、马尔科夫过程、主方程、生成函数等。在第二章,我们基于少数者获胜的原则以及从众的行为机制,建立了一个描述个体竞争多个资源的少数者博弈模型。通过对模型的研究,我们发现多种资源根据其使用率的变化特征自发地分组,并显现出震荡行为。这些结果显示系统低效率的潜在原因是资源的分组震荡。此外,我们提出了描述该过程的数学框架,包括基于不考虑拓扑结构的平均场描述,以及考虑了个体间连接稀疏性的修正平均场描述,分别得到了与模拟相吻合的解析结果。此外,我们在股市中也观察到了个股收益分组震荡的现象,并对真实系统中大量出现的类似行为做了讨论。该工作所建立的理论将有助于真实社会系统中的资源竞争、优化分配等问题的研究。在第三章,我们提出并建立了一种很直观的控制方法——钉扎控制,用以控制个体基于可得到的信息选择利用率低的资源引发的羊群行为。该行为常常导致大多数个体拥挤并竞争个别的资源而其他资源空闲的结果。钉扎控制的方法能够非常有效地抑制资源分配动力学过程中的羊群行为。我们发现仅仅通过固定(钉扎)很少数个体对资源的选择性,而保留大多数个体能够自由选择资源,就能够消除羊群行为。我们系统地研究了随机钉扎和倾向性钉扎等钉扎策略、全连接图和无标度网络等个体相互作用网络结构下的钉扎控制过程,并且提出了基于平均场理论框架下的完全的解析理论来帮助理解控制的实现机制。在第四章,我们针对不同钉扎模式下钉扎调控是否有助于资源配置的优化进行了更为广泛的探讨。在研究中,我们发现对于给定的具有一定异质性的网络中,在异化的相互作用方式下,存在一个独立于钉扎模式的最优钉扎密度。在该钉扎密度下,系统的资源配置得到了最大程度的优化。随后,我们发展了一套理论用以解释最优钉扎密度的涌现,并预测了最优钉扎密度对网络拓扑结构的依赖关系。这些工作为存在少数者博弈机制的复杂动力系统中涨落等问题的研究提供给了一个基本的、普遍的框架,这对社会、生态以及政治体系中相关问题的研究有重要的启发和潜在的应用价值。在第五章,鉴于社会系统中合作往往以混合策略的形式出现,我们将经典的囚徒困境博弈与观点博弈相结合构造了一个超对策博弈的演化动力学模型,该模型中个体的决策由自身对博弈的观点决定。通过数值模拟,系统出现了以混合策略形式涌现的合作现象,此外,我们根据模拟的部分结果给出了以混合策略形式出现的高合作比例所需的条件进而分析出不同参数对该条件的影响。通过对参数的分析,可得知较温和的社会环境、个体对虚假信息的较强警惕性能促进高合作比例的混合策略的涌现。这些结果有利于促进我们对真实社会系统个体之间相互作用形式的理解,具有一定现实意义。在第六章,我们对已有的工作进行了总结,并对未来的研究方向和研究思路进行了展望。
[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.

【学位授予单位】：兰州大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：N941.4
，

本文编号：1374554