AI 中文总结
针对对手持续优化混合压力的问题，提出耦合动力系统模型，证明均衡存在性与稳定性，并通过伊朗认知战案例验证，计算其与崩溃边界的距离。
AI 中文摘要
一个防御国面临来自对手持续的经济、媒体和心理压力，而对手不断重新优化其行动，这构成了运筹学中现有攻击者-防御者模型无法直接解决的问题，因为这些模型将防御者的状态视为离散分配而非连续的、缓慢变化的制度过程。我们构建了一个耦合动力系统，其中不满和制度韧性连续演化，而压力强度由优化的马尔可夫决策过程选择，证明了所得均衡的存在性和局部稳定性，并给出了一个形式化结果，将其与标准反馈稳定性分析以及孤立处理的平稳马尔可夫链区分开来。我们使用三十个随机网络实例、全值迭代以及一个关于针对伊朗（2017-2026）的认知战案例研究对框架进行了计算验证。历史校准的案例大约位于计算出的操作崩溃边界上方二十五倍处，而贪婪播种策略在随机实例中平均达到百分之八十七的网络渗透率，显著高于度中心性基线。实践者可以使用均衡和边界计算来评估特定案例相对于崩溃的位置，而不是依赖对手压力强度之间的未经验证的比较。
英文摘要
A defending state facing sustained economic, media, and psychological pressure from an adversary that continuously re-optimises its campaign poses a problem that existing attacker-defender models in operations research do not directly resolve, because they treat the defender's state as a discrete allocation rather than a continuous, slow-moving institutional process. We formulate a coupled dynamical system in which grievance and institutional resilience evolve continuously while pressure intensity is chosen by an optimising Markov decision process, prove existence and local stability of the resulting equilibrium, and prove a formal result distinguishing it from standard feedback-stability analysis and from a stationary Markov chain treated in isolation. We validate the framework computationally using thirty randomised network instances, full value iteration, and a documented case study of cognitive warfare directed at Iran (2017--2026). The historically calibrated case sits approximately twenty-five times above the computed operational collapse boundary, and a greedy seeding policy reaches eighty-seven percent average network penetration across the randomised instances, significantly above a degree-centrality baseline. A practitioner can use the equilibrium and boundary computation to assess where a specific case sits relative to collapse, rather than relying on an unverified comparison between opposing pressure intensities.
CommentsI noticed some methodological issues
