线性基于代理系统的一般化 Langevin 模型：通过环境耦合实现战略影响
Generalized Langevin Models of Linear Agent-Based Systems: Strategic Influence Through Environmental Coupling
AI总结：
本文提出了一种基于一般化 Langevin 方程的线性代理系统模型，通过环境耦合揭示记忆效应和战略影响机制。
摘要：
基于代理的模型通常将系统孤立处理，将环境耦合视为计算上不可行或动态上无关的。我们证明这种忽视遗漏了本质物理：环境自由度会产生记忆效应，从根本上改变系统动力学。通过系统地将线性更新规则转换为精确的一般化 Langevin 方程，我们表明未观察到的环境代理表现为记忆核，其时间尺度和耦合强度由环境相互作用频谱决定。网络拓扑以不同方式塑造这种记忆结构：小世界重排使动力学向单一主导弛豫模式发展，而碎片化环境维持多个持久模式，对应于孤立子群体。我们应用此框架于隐蔽影响操作，其中对手通过环境中介者单独操控目标群体。稳态响应可通过击中概率解释，揭示了狂热意见如何通过环境扩散，使系统代理意见向狂热者均值偏移——即使狂热者从未直接接触目标。
英文摘要：
Agent-based models typically treat systems in isolation, discarding environmental coupling as either computationally prohibitive or dynamically irrelevant. We demonstrate that this neglect misses essential physics: environmental degrees of freedom create memory effects that fundamentally alter system dynamics. By systematically transforming linear update rules into exact generalized Langevin equations, we show that unobserved environmental agents manifest as memory kernels whose timescales and coupling strengths are determined by the environmental interaction spectrum. Network topology shapes this memory structure in distinct ways: small-world rewiring drives dynamics toward a single dominant relaxation mode, while fragmented environments sustain multiple persistent modes corresponding to isolated subpopulations. We apply this framework to covert influence operations where adversaries manipulate target populations exclusively via environmental intermediaries. The steady-state response admits a random-walk interpretation through hitting probabilities, revealing how zealot opinions diffuse through the environment to shift system agent opinions toward the zealot mean - even when zealots never directly contact targets.
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