提出连续时间记忆系统，用经济机制与物理记忆协同实现稳定闭环控制。
Feedback-Coupled Memory Systems in Continuous Time
- 用价格机制和物理记忆定义动态更新规则，实现去中心化协调。
- 证明系统全局耗散性，阈值条件为 $4β^2 < 2ημγ^2$。
- 适用于多智能体系统、自组织控制，尤其关注稳定性边界分析。
反馈耦合记忆系统（FCMS）通过四个抽象算子形式化闭环协作，其中代理更新算子 $f_i$ 和环境更新算子 $Ψ$ 在原始框架中未明确定义。本文通过机制型智能（MBI）定义 $f_i$，使代理基于去中心化价格机制与经济原则本地更新；通过耦合记忆图过程（CMGP）定义 $Ψ$，将环境视为可记录并一致响应轨迹历史的物理基底，无需外部驱动。由此构建的连续时间FCMS实例满足由可计算阈值 $4β^2 < 2ημγ^2$ 控制的李雅普诺夫全局耗散性。该结果同时推广了离散FCMS的稳定性条件 $4ηβ^2 < γ$ 与CMGP的物理分岔阈值 $α_c = 1/K$，验证了‘记忆耗散必须快于反馈增益’这一普遍组织原则。数值模拟在 $N=2$ 个代理下确认稳定性阈值，均场验证在 $N=10^6$ 下揭示当阈值被突破时出现自我强化的协调级联现象。
原文摘要 · Abstract (English)
The Feedback-Coupled Memory Systems (FCMS) architecture formalizes closed-loop coordination through four abstract operators, two of which - the agent update operator $f_i$ and the environmental update operator $Ψ$ - are left axiomatically undefined in the original framework. To address this, $f_i$ is defined by Mechanism-Based Intelligence (MBI), where agents update locally through a decentralized price mechanism and economic principles, and $Ψ$ is defined by the Coupled Memory Graph Process (CMGP), a non-Markovian framework where the environment is treated as a physical substrate that records and responds to trajectory history coherently without external forcing. The resulting continuous-time FCMS instantiation achieves Lyapunov global dissipativity governed by the computable threshold $4β^2 < 2ημγ^2$. This generalizes both the discrete FCMS stability condition $4ηβ^2 < γ$ and CMGP's physical bifurcation threshold $α_c = 1/K$, confirming that memory dissipation must outpace feedback gain as a universal organizing principle. Numerical simulation with $N=2$ agents and mean-field validation at $N=10^6$ confirm the stability threshold and the self-reinforcing coordination cascade that emerges when it is violated.
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