异质网络中的意见动态：收敛猜想与定理
Opinion Dynamics in Heterogeneous Networks: Convergence Conjectures and Theorems
摘要：
近年来，观点动态模型受到了广泛的关注，在该模型中，观点由实数描述，主体通过平均邻居的观点来同步更新自己的观点。每个代理的邻居可以被定义为（1）那些代理的意见是在其“置信范围”，或（2）那些代理的“影响范围”包含代理的意见。前一个定义是Hegselmann和Krause的有界置信模型中采用的，而后者是新的。由于每个代理的置信度和影响范围不同，异构的状态依赖的互连拓扑结构导致了一个很难理解的复杂的动态行为。在这两个模型中，我们通过他们的互连拓扑结构的代理进行分类，并相应地，计算系统的平衡。然后，我们定义了一个积极的不变集中在每个均衡意见向量。我们表明，如果一个轨迹进入一个这样的集合，那么它收敛到一个稳定的状态与恒定的互连拓扑结构。这个结果给了我们一个新的充分条件，这两个模型建立收敛，并符合我们的猜想，所有的轨迹的有界置信度和影响力模型最终收敛到一个稳定的状态下固定的拓扑结构。
英文摘要：
Recently, significant attention has been dedicated to the models of opinion dynamics in which opinions are described by real numbers, and agents update their opinions synchronously by averaging their neighbors' opinions. The neighbors of each agent can be defined as either (1) those agents whose opinions are in its "confidence range," or (2) those agents whose "influence range" contain the agent's opinion. The former definition is employed in Hegselmann and Krause's bounded confidence model, and the latter is novel here. As the confidence and influence ranges are distinct for each agent, the heterogeneous state-dependent interconnection topology leads to a poorly-understood complex dynamic behavior. In both models, we classify the agents via their interconnection topology and, accordingly, compute the equilibria of the system. Then, we define a positive invariant set centered at each equilibrium opinion vector. We show that if a trajectory enters one such set, then it converges to a steady state with constant interconnection topology. This result gives us a novel sufficient condition for both models to establish convergence, and is consistent with our conjecture that all trajectories of the bounded confidence and influence models eventually converge to a steady state under fixed topology.
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。
