【作者】 张晓丹；

【导师】 贺明峰；

【作者基本信息】 大连理工大学 ， 应用数学， 2012， 硕士

【摘要】 在近些年来,基于统计物理学的社会学研究被研究学者们广泛关注。其中包括：意见传播动力学,语言动力学及舆论传播动力学等等。在本文中,首先介绍了相关动力学的基本模型和结论,包括意见传播动力学及在此基础上发展而来的符号动力学命名博弈。异质性在遗传学和生态学中很常见,而在实际中,其实在社会学中也广泛存在,它是“同质化”的对立面,主要意思是非均匀性或者是复杂性。在本文中,我们分别在意见传播动力学和命名博弈中引入异质性的概念,并讨论异质性对社会动力学的影响。在本文的第二章主要讨论异质性对意见传播动力学的影响,在Voter模型中引入冰冻期的概念,个体在冰冻期内接受邻居个体意见的概率很小。在表面上冰冻期的引入使得个体改变意见更难,然而通过计算机模拟发现对于不同大小的群体,会存在一个和系统大小相关冰冻期长度----使得系统中意见统一的时间最短。这一现象的出现说明了冰冻期的引入在一定状况下是加速了系统的统一。在第二章的具体讨论中,我们详细讨论了冰冻期对于意见传播动力学中一些微观量的影响：磁化率、意见团簇的大小及个体空间分布图等。同时,文中还使用马尔科夫过程理论分析了冰冻期加速意见统一过程的原理,进而证实了正确性。基于Voter意见传播模型的研究有很多,命名博弈就是Voter模型的一个变形,目前已经属于符号动力学的研究领域。在本文中,在命名博弈模型中加入了可以体现词汇异质性的多样性。通过对不同的词汇赋予不同的权重作为词汇的异质性,在模型中我们着重考虑了三种不同的多样性分布——均匀分布、指数分布和幂分布。在个体之间的交流中,词汇多样性会直接影响词汇选择的概率。计算机模拟结果显示这种多样性的引入可以加速一致性的达成。在结果中,通过讨论命名博弈中的词汇总量、不同词汇量及交流成功率,从微观上了解多样性对结果的存进作用。同时文中还讨论了在复杂网络上的模型结果,结果显示：模型的实验结果对于不同的拓扑结果是稳定的。通过在两种社会动力学模型中引入异质性的概念,看似使模型变得更为复杂,使得系统更加无序,而实验结果却表明了异质性往往可以促进系统有序的形成。更多还原

【Abstract】 Recently, the study of collective behavior has received growing attention in statistical physics, economics and sociology. Social dynamics, as an important aspect, include opinion dynamics, language evolution and competition. In this paper, we firstly introduced some basic models and some fruitful results of the models, which mainly focus on the opinion dynamics and a recently developed language model, naming game. In this paper, heterogeneous beliefs are considered, which is popular in biology and sociology.In the second section, we study voter model with the consideration of freezing period, in which the probability of changing opinion is small. Interestingly, we find that there exists an optimal value of freezing time, leading to the shortest consensus time. This phenomenon can be greatly validated by the evolution of opinion formation. We provide the explanation of this effect from both the number of changing opinion and the number of opinion clusters, and find that the feedback mechanism and fast formation of effective clusters induced by the optimal freezing time are the promotion factors. Moreover, the impact of other quantities, such as the overall number of opinions and the probability of changing opinion, is also studied. The result is also proved by mathematical method. Our results will be helpful for better understanding and exploring the existence of collective behavior in other research fields.Many modified versions of the voter model have been proposed to study the social dynamics. The naming game which is belong to language game, also related to the opinion formation, has been considered as an important approach to understand the evolution of a language or communication behaviors among a population of agents. In the third section, we introduce word diversity that reflects the heterogeneity of words into the naming game. Diversity is realized by assigning a weight factor to each word. The weight is determined by three distributions (uniform, exponential and power-law distributions). During the communication, the probability that a word is selected from speaker’s memory depends on the introduced word diversity. Interestingly, we find that the word diversity following three different distributions can remarkably promote the final convergence, which is of high importance in the self-organized system. We provide an explanation of this effect based on both the number of different names and the number of total names, and find that a wide spread of names induced by the segregation of words is the main promotion factor.更多还原