The Effect Of Heterogeneity On Social Dynamics

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.