Abstract We propose and analyze a stochastic model for opinion dynamics over social networks. In the scenario considered, each agent has an opinion level which belongs to a discrete set. At any given time, the agent takes an action 0 or 1 depending on the opinion, and this action can be seen as a binary signal that can influence the other agents in the network. The opinion updates based on the signal from a random neighbor or from an external entity who attempts to manipulate or control the network. In the absence of the external signal or a constant signal, this model is shown to asymptotically produce consensus with a finite number of connected agents. Additionally, the consensus is determined by the signal. On the other hand, when the number of agents is large, the time to achieve consensus can become exponentially large and the dynamics exhibit population equilibrium points that are ”metastable”. These equilibria can be observed with a finite (but large) number of agents through numerical simulations and are shown to persist for a long duration.

中文翻译：

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二元外生和内生信号下的舆论动态分析

摘要 我们提出并分析了社交网络上意见动态的随机模型。在所考虑的场景中，每个代理都有一个属于离散集的意见级别。在任何给定的时间，代理根据意见采取行动 0 或 1，并且该行动可以被视为可以影响网络中其他代理的二元信号。意见更新基于来自随机邻居或试图操纵或控制网络的外部实体的信号。在没有外部信号或恒定信号的情况下，该模型显示出与有限数量的连接代理渐近地产生共识。此外，共识是由信号决定的。另一方面，当代理数量较多时，达成共识的时间可能会呈指数级增长，并且动态表现出“亚稳态”的种群平衡点。这些平衡可以通过数值模拟用有限（但大量）数量的代理观察到，并且显示出持续很长时间。