局部与全局交互作用下外生输入与违抗主体对观点动力学的影响
The Effect of Exogenous Inputs and Defiant Agents on Opinion Dynamics with Local and Global Interactions
摘要：
大多数传统的观点动力学模型主要考虑了完全局部的影响，即近视的代理人在与邻近的其他代理人交互后决定他们的行为。例如，在社交互动的情况下，这包括家庭，朋友和其他强大的社会关系。本文中提出的模型也体现了全球影响力，其中，全球意味着每个节点也观察到整个人群的平均行为样本（在社会示例中，人们观察街道上的其他人，地铁和其他社交场所）。我们考虑节点具有二分状态的情况（示例包括两个主要政党的选举，是否采用新技术或产品，以及任何是/否意见，例如在全民公决中投票）。研究了具有任意度分布网络的状态动力学。对于给定的初始条件，我们找到了在每个状态上达成共识的概率和达到共识的期望时间。研究了系统的平均取向上的外生偏差的影响，以模拟大众媒体。为此，我们向模型中添加一个外部场，使其中一个状态优于另一个状态。该字段干扰每个节点的常规决策过程，并创建倾向于其中一个状态的恒定概率。对于给定的初始条件，我们求解系统的平均状态作为时间的函数。然后，反顺从者（从不修改其状态的顽固节点）被添加到网络中，以规避外部偏见。我们找到了必要的条件，这些违抗节点的数量需要取消外部偏见的影响。我们的分析是基于平均场近似的代理人的意见。
英文摘要：
Most of the conventional models for opinion dynamics mainly account for a fully local influence, where myopic agents decide their actions after they interact with other agents that are adjacent to them. For example, in the case of social interactions, this includes family, friends, and other strong social ties. The model proposed in this contribution, embodies a global influence as well where, by global, we mean that each node also observes a sample of the average behavior of the entire population (in the social example, people observe other people on the streets, subway, and other social venues). We consider a case where nodes have dichotomous states (examples include elections with two major parties, whether or not to adopt a new technology or product, and any yes/no opinion such as in voting on a referendum). The dynamics of states on a network with arbitrary degree distribution are studied. For a given initial condition, we find the probability to reach consensus on each state and the expected time reach to consensus. The effect of an exogenous bias on the average orientation of the system is investigated, to model mass media. To do so, we add an external field to the model that favors one of the states over the other. This field interferes with the regular decision process of each node and creates a constant probability to lean towards one of the states. We solve for the average state of the system as a function of time for given initial conditions. Then anti-conformists (stubborn nodes who never revise their states) are added to the network, in an effort to circumvent the external bias. We find necessary conditions on the number of these defiant nodes required to cancel the effect of the external bias. Our analysis is based on a mean field approximation of the agent opinions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
