社会群体态度形成的确定性模型中的非周期动力学
Aperiodic dynamics in a deterministic model of attitude formation in social groups
摘要：
同质性和社会影响是推动社会群体内态度、信仰和行为演变的基本机制。同质性将个体的态度状态对之间的相似性与他们的互动频率联系在一起，从而产生结构性联系强度，而社会影响则导致个体在互动过程中的状态趋同。基于这些基本要素，我们提出了一个新的数学建模框架来描述一组相互作用的代理人的态度的演变。具体来说，我们的模型描述了具有激活-抑制关系的潜意识态度。我们考虑一个均匀的人口使用确定性，连续时间动力系统。令人惊讶的是，同质性和社会影响力的综合效应并不一定会导致群体共识或全球单一文化。我们观察到，子组的形成和极化效应可能是短暂的，长时间的动力学是准周期性的敏感依赖于初始条件。这是由于不断发展的互动网络和图灵不稳定性与态度状态动态之间的相互作用。
英文摘要：
Homophily and social influence are the fundamental mechanisms that drive the evolution of attitudes, beliefs and behaviour within social groups. Homophily relates the similarity between pairs of individuals' attitudinal states to their frequency of interaction, and hence structural tie strength, while social influence causes the convergence of individuals' states during interaction. Building on these basic elements, we propose a new mathematical modelling framework to describe the evolution of attitudes within a group of interacting agents. Specifically, our model describes sub-conscious attitudes that have an activator-inhibitor relationship. We consider a homogeneous population using a deterministic, continuous-time dynamical system. Surprisingly, the combined effects of homophily and social influence do not necessarily lead to group consensus or global monoculture. We observe that sub-group formation and polarisation-like effects may be transient, the long-time dynamics being quasi-periodic with sensitive dependence to initial conditions. This is due to the interplay between the evolving interaction network and Turing instability associated with the attitudinal state dynamics.
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