激进派得票率动态单纯形模型中的阈值下双稳态与实施滞后
Below-threshold Bistability and Implementation Lag in a Simplex Model of Radical Vote-Share Dynamics
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中文总结 AI 辅助
本文针对政策实施延迟下的激进派得票率动态构建单纯形非自治隔室模型，揭示了阈值下双稳态与实施滞后现象，分析了相关阈值特征与延迟界，指出阈值恢复具有预防性。
中文摘要 AI 辅助
我们研究了一个关于概率单纯形的非自治隔室模型，用于分析政策实施延迟情况下的激进派得票率动态。该模型区分了目标政权与以有限速度调整的有效政权，其中包含一个可被激进派后续动员的持续异化储备库。在对称基准情形下，持续的异化破坏了全局单阈值图景：在局部不稳定性阈值以下，无激进派的中间派—异化均衡可能与稳定的正均衡共存，二者被鞍结分岔产生的鞍分支分隔。通过双曲持久性，这种共存状态在对称基线附近得以保留，而数值探索则发现在非对称扰动下存在更宽的双稳态区域。延迟实施进一步分离了目标与有效阈值的通过过程，在激进派支持率出现可见响应前，产生了参数空间滞后与额外的状态空间滞后。分析结合了冻结无激进派均衡的Perron-Frobenius阈值、正均衡的几何特征、慢均匀亚临界漂移下的局部绝热跟踪，以及横向阈值通过的显式延迟界。在初始匹配条件下，参数空间延迟的尺度为O(κ_θ⁻¹)；在单调斜坡示例中，该界几乎达到，而状态空间滞后则大得多且对实施速度的敏感性较低。因此，阈值恢复是预防性而非治疗性的：一旦轨迹进入激进化吸引子的吸引域，即使回到局部阈值以下也未必能恢复无激进派政权。
英文摘要
We study a nonautonomous compartmental model on the probability simplex for radical vote-share dynamics under delayed policy implementation. The model distinguishes a target regime from an effective regime that adjusts with finite speed and includes a persistent alienation reservoir that can later be mobilised by radical actors. In a symmetric benchmark, persistent alienation destroys the global one-threshold picture: below the local instability threshold, a radical-free centrist--alienated equilibrium may coexist with a stable positive equilibrium, separated by a saddle branch created in a saddle-node bifurcation. By hyperbolic persistence, this coexistence survives near the symmetric baseline, while numerical exploration identifies a wider bistable region under asymmetric perturbations. Delayed implementation further separates target and effective threshold passage, producing a parameter-space lag and an additional state-space lag before a visible response in radical support. The analysis combines a Perron--Frobenius threshold for the frozen radical-free equilibrium, a geometric characterisation of positive equilibria, local adiabatic tracking under slow uniformly subcritical drift, and explicit delay bounds for transversal threshold passage. Under initial matching, the parameter-space delay scales as \(O(κ_θ^{-1})\); in a monotone ramp example the bound is nearly attained, whereas the state-space lag is substantially larger and less sensitive to implementation speed. Thus threshold restoration is preventive rather than curative: once the trajectory enters the basin of the radicalised attractor, returning below the local threshold need not restore the radical-free regime.
