标题： 动态网络上的非线性传播动力学：从共识时间到演化轨迹的精确解 显示英文标题

标题： Nonlinear contagion dynamics on dynamical networks: exact solutions ranging from consensus times to evolutionary trajectories

摘要： 理解动态网络上的非线性社会传染动力学（如意见形成）对于深入了解共识与极化至关重要。与依赖阈值的复杂传播类似，采纳率中的非线性给平均场近似带来了挑战。 为了解决这一理论空白，我们专注于动态网络上的非线性二元意见动力学，并解析推导局部配置，特别是特定焦点个体邻域内意见的分布。 这种精确的意见局部配置，结合网络度分布，使我们能够获得关于共识时间和演化轨迹的精确解。 我们的反直觉结果显示，无论是有偏同化（即非线性采纳率），还是局部网络重连的偏好——例如群体内偏见（倾向于志趣相投的个体）和马太效应（倾向于社交中心节点）——都无法显著减缓共识的达成。 在这三个社会因素中，我们发现有偏同化对加速共识的影响最大。 此外，我们的分析方法高效且精确地预测了由非线性传播动力学引发的采纳曲线的演化轨迹。 我们的工作为超越意见形成的通用非线性传播动力学的分析预测铺平了道路。 显示英文摘要

摘要： Understanding nonlinear social contagion dynamics on dynamical networks, such as opinion formation, is crucial for gaining new insights into consensus and polarization. Similar to threshold-dependent complex contagions, the nonlinearity in adoption rates poses challenges for mean-field approximations. To address this theoretical gap, we focus on nonlinear binary-opinion dynamics on dynamical networks and analytically derive local configurations, specifically the distribution of opinions within any given focal individual's neighborhood. This exact local configuration of opinions, combined with network degree distributions, allows us to obtain exact solutions for consensus times and evolutionary trajectories. Our counterintuitive results reveal that neither biased assimilation (i.e., nonlinear adoption rates) nor preferences in local network rewiring -- such as in-group bias (preferring like-minded individuals) and the Matthew effect (preferring social hubs) -- can significantly slow down consensus. Among these three social factors, we find that biased assimilation is the most influential in accelerating consensus. Furthermore, our analytical method efficiently and precisely predicts the evolutionary trajectories of adoption curves arising from nonlinear contagion dynamics. Our work paves the way for enabling analytical predictions for general nonlinear contagion dynamics beyond opinion formation.