AI 中文总结
该研究提出含记忆丢失与通信延迟的观点动力学框架，引入相对偏差与时滞动力系统，扩展至含机器人的网络并量化其影响，经仿真验证各因素对观点演化的作用。
AI 中文摘要
我们提出了一个新颖的框架，用于建模通过加权有向网络连接的个体的二元观点（0或1），其中边权重量化了人际影响。与假设可完全获取先前表达观点的经典模型不同，我们的框架允许个体使用结构化记忆集更新其偏差，该记忆集捕捉有限且延迟的信息交换。为分析这些观点差异，我们引入了数学上易处理的个体间相对偏差概念，相对偏差根据包含记忆集指定的过去表达观点的线性更新规则演化。我们将个体的信念定义为表达观点1的概率，并推导出控制网络信念演化的时滞动力系统，确定其渐近行为并表征其性质。该框架进一步扩展到包含机器人（bots）的网络，机器人维持固定偏差同时影响相邻个体，我们通过比较存在和不存在机器人时动力系统的不动点来量化机器人的影响。最后，仿真说明记忆、网络结构和机器人交互对所得观点动力学的影响。
英文摘要
We propose a novel framework for modeling binary opinions (0 or 1) of individuals connected through a weighted directed network, where edge weights quantify interpersonal influence. Unlike classical models that assume complete access to previously expressed opinions, our framework allows individuals to update their biases using structured memory sets that capture limited and delayed information exchange. To analyze these opinion differences, we introduce a mathematically tractable notion of relative bias between pairs of individuals. The relative biases evolve according to a linear update rule involving past expressed opinions specified by the memory sets. We define the belief of an individual as the probability of expressing opinion 1 and derive a time-delayed dynamical system governing the evolution of network beliefs. We establish its asymptotic behavior and characterize its properties. The framework is further extended to networks containing bots, which maintain fixed biases while influencing neighboring individuals. We quantify the effect of bots by comparing the fixed points of the dynamics in their presence and absence. Finally, simulations illustrate the influence of memory, network structure, and bot interactions on the resulting opinion dynamics.
Comments35 pages, 2 tables, 12 figures
