Quantum Fields LLC, St. Charles, IL, United States of America.
Windsong Associates, Richland Center, WI, United States of America.
PLoS One. 2021 Nov 16;16(11):e0259625. doi: 10.1371/journal.pone.0259625. eCollection 2021.
The model is based on a vector representation of each agent. The components of the vector are the key continuous "attributes" that determine the social behavior of the agent. A simple mathematical force vector model is used to predict the effect of each agent on all other agents. The force law used is motivated by gravitational force laws and electrical force laws for dipoles. It assumes that the force between two agents is proportional to the "similarity of attributes", which is implemented mathematically as the dot product of the vectors representing the attributes of the agents, and the force goes as the inverse square of the difference in attributes, which is expressed as the Euclidean distance in attribute space between the two vectors. The force between the agents may be positive (attractive), zero, or negative (repulsive) depending on whether the angle between the corresponding vectors is less than, equal to, or greater than 90°. A positive force causes the attributes of the agents to become more similar and the corresponding vectors to become more nearly parallel. Interaction between all agents is allowed unless the distance between the attributes representing the agents exceeds a confidence limit (the Attribute Influence Bound) set in the simulation. Agents with similar attributes tend to form groups. For small values of the Attribute Influence Bound, numerous groups remain scattered throughout attribute space at the end of a simulation. As the Attribute Influence Bound is increased, and agents with increasingly different attributes can communicate, fewer groups remain at the end, and the remaining groups have increasingly different characteristic attributes and approximately equal sizes. With a large Attribute Influence Bound all agents are connected and extreme bi- or tri-polarization results. During the simulations, depending on the initial conditions, collective behaviors of grouping, consensus, fragmentation and polarization are observed as well as certain symmetries specific to the model, for example, the average of the attributes for all agents does not change significantly during a simulation.
该模型基于每个主体的向量表示。向量的分量是决定主体社会行为的关键连续“属性”。使用简单的数学力向量模型来预测每个主体对所有其他主体的影响。所使用的力定律受万有引力定律和偶极子的电动力定律启发。它假设两个主体之间的力与“属性相似性”成正比，这在数学上实现为表示主体属性的向量的点积，力与属性差异的平方成反比，这在属性空间中表示为两个向量之间的欧几里得距离。主体之间的力可以是正（吸引）、零或负（排斥），具体取决于对应向量之间的夹角小于、等于或大于 90°。正力会使主体的属性变得更加相似，相应的向量变得更加平行。除非代表主体的属性之间的距离超过模拟中设置的置信限（属性影响边界），否则允许所有主体相互作用。具有相似属性的主体倾向于形成群体。对于属性影响边界的较小值，在模拟结束时，大量群体仍然分散在属性空间中。随着属性影响边界的增加，并且具有越来越不同属性的主体可以进行通信，在模拟结束时留下的群体越来越少，并且剩余的群体具有越来越不同的特征属性和大致相等的大小。当属性影响边界较大时，所有主体都连接在一起，导致极端的双极或三极极化。在模拟过程中，根据初始条件，会观察到分组、共识、分裂和极化等集体行为，以及模型特有的某些对称性，例如，所有主体的属性平均值在模拟过程中不会发生显著变化。
