Trust is the invisible glue that holds together the fabric of societies, economic systems, and political institutions. Yet, its dynamics-especially in real-world settings remain unpredictable and difficult to control. While classical trust game models largely rely on discrete frameworks with limited noise, they fall short in capturing sudden behavioral shifts, extreme volatility, or abrupt breakdowns in cooperation.Here, we propose-for the first time a comprehensive stochastic model of trust based on Lévy processes that integrates three fundamental components: Brownian motion (representing everyday fluctuations), Poissonian jump intensity (capturing the frequency of shocks), and random distributions for jump magnitudes. This framework surpasses conventional models by enabling simulations of phenomena such as "sudden trust collapse," "chaotic volatility," and "nonlinear recoveries" dynamics often neglected in both theoretical and empirical studies.By implementing four key simulation scenarios and conducting a detailed parameter sensitivity analysis via 3D and contour plots, we demonstrate that the proposed model is not only mathematically more advanced, but also offers a more realistic representation of human dynamics compared to previous approaches. Beyond its technical contributions, this study outlines a conceptual framework for understanding fragile, jump-driven behaviors in social, economic, and geopolitical systems-where trust is not merely a psychological construct, but an inherently unstable and stochastic variable best captured through Lévy based modeling.

翻译：信任是维系社会结构、经济体系与政治制度的无形纽带。然而，其动态特性——尤其在现实场景中——仍具有不可预测性与难以控制性。经典信任博弈模型主要依赖噪声有限的离散框架，难以捕捉合作中突发行为转变、极端波动或骤然崩溃等现象。本文首次提出基于Lévy过程的综合随机信任模型，该模型整合了三个基本组成部分：布朗运动（表征日常波动）、泊松跳跃强度（捕捉冲击频率）以及跳跃幅度的随机分布。该框架通过模拟"信任骤降"、"混沌波动"与"非线性恢复"等现象，超越了传统模型的局限——这些动态在理论与实证研究中常被忽视。通过实施四种关键模拟场景，并借助三维与等高线图进行详细的参数敏感性分析，我们证明所提模型不仅数学上更为先进，相较于既有方法还能更真实地反映人类行为动态。除技术贡献外，本研究构建了理解社会、经济与地缘政治系统中脆弱跳跃驱动行为的概念框架——在这些系统中，信任不仅是心理建构，更是本质上不稳定且宜用Lévy建模描述的随机变量。