用图扩散与随机漂移建模经济网络中节点生存动态，揭示稳定性临界点。
The Graph-Embedded Hazard Model (GEHM): Stochastic Network Survival Dynamics on Economic Graphs
- 将图 $p$-拉普拉斯扩散与随机漂移结合，构建非线性演化模型
- 发现枢纽节点加剧非线性梯度，压缩稳定区间并导致重尾生存分布
- 适用于研究金融系统、供应链等复杂网络的脆弱性与突变风险
本文提出一种非线性演化框架，用于建模加权经济网络上的生存动态。通过耦合基于图的 $p$-拉普拉斯扩散算子与随机结构漂移，构建有限维偏微分-随机微分方程系统，刻画节点生存如何响应非线性扩散压力，同时聚合复杂度因子遵循伊藤过程演化。利用增生算子理论、非线性半群方法与随机分析，证明了温和解的存在唯一性，导出依赖拓扑的能量耗散不等式，并刻画了分离耗散、临界、放大与爆炸区间的稳定性阈值。在巴尔巴西-阿尔伯特网络上的数值实验表明，枢纽节点增强非线性梯度，压缩稳定性边界，产生重尾生存分布并引发偶发爆炸行为。
原文摘要 · Abstract (English)
This paper develops a nonlinear evolution framework for modelling survival dynamics on weighted economic networks by coupling a graph-based $p$-Laplacian diffusion operator with a stochastic structural drift. The resulting finite-dimensional PDE--SDE system captures how node-level survival reacts to nonlinear diffusion pressures while an aggregate complexity factor evolves according to an Itô{} process. Using accretive operator theory, nonlinear semigroup methods, and stochastic analysis, we establish existence and uniqueness of mild solutions, derive topology-dependent energy dissipation inequalities, and characterise the stability threshold separating dissipative, critical, amplifying, and explosive regimes. Numerical experiments on Barabási--Albert networks confirm that hub dominance magnifies nonlinear gradients and compresses stability margins, producing heavy-tailed survival distributions and occasional explosive behaviour.
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