AI 中文总结
研究社会规范扩散的最小动力学模型，个体在三种状态转变，呈现潜伏-爆发动态模式。通过分析平衡点等条件确定产生孵化现象的非线性机制并推导潜伏期估计值，揭示由内部相互作用驱动社会变革的动力学途径。
AI 中文摘要
在本文中，我们引入了一个用于新社会规范扩散的最小动力学模型，其中个体在三种状态之间转变：非支持者、沉默支持者和发声倡导者。尽管该模型简单且与经典的SI型和SIS型传播动力学密切相关，但它展现出一种非平凡的潜伏-爆发动态模式：初始的小采用波之后是长时间的静止期，然后是支持的突然内源性爆发。通过对平衡点、稳定性、收敛性和相变条件的完整分析表征，我们确定了产生这种孵化现象的非线性机制并推导了潜伏期的估计值。我们的结果揭示了一条纯粹由内部相互作用而非外部冲击驱动的突然社会变革的动力学途径。
英文摘要
In this paper, we introduce a minimal dynamical model for the diffusion of a new social norm, in which individuals transition among three states: non-supporters, silent supporters, and vocal advocates. Despite its simplicity and its close relation to the classical SI-type and SIS-type spreading dynamics, this model exhibits a nontrivial latent-outbreak dynamic pattern: an initial small adoption wave is followed by a long quiescent period and then an abrupt, endogenous explosion of support. Through a complete analytical characterization of equilibria, stability, convergence, and phase-transition conditions, we identify the nonlinear mechanism that generates this incubation phenomenon and derive estimates of the latent period. Our results reveal a dynamical route to sudden social change driven purely by internal interactions rather than external shocks.
