AI 中文总结
研究反馈耦合记忆系统，通过基于机制的智能和耦合记忆图过程分别定义未明确的代理更新算子和环境更新算子，推广了离散FCMS稳定性条件等，实现连续时间FCMS实例的李雅普诺夫全局耗散性，数值模拟和验证证实相关结论。
AI 中文摘要
反馈耦合记忆系统（FCMS）架构通过四个抽象算子形式化闭环协调，其中原始框架中代理更新算子$f_i$和环境更新算子$\Psi$未明确界定。为此，$f_i$由基于机制的智能（MBI）定义，代理通过分散价格机制和经济原则进行局部更新；$\Psi$由耦合记忆图过程（CMGP）定义，环境被视为记录和响应轨迹历史的物理基质。所得连续时间FCMS实例实现了由可计算阈值$4\beta^2 < 2\eta\mu\gamma^2$控制的李雅普诺夫全局耗散性。这推广了离散FCMS稳定性条件和CMGP的物理分岔阈值，证实记忆耗散必须超过反馈增益作为通用组织原则。数值模拟和平均场验证证实了稳定性阈值及违反时出现的自增强协调级联。
英文摘要
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.
Comments19 pages, 4 figures. Extends arXiv:2603.11560 to continuous time. Code: github.com/stevefatz95/fcms-continuous
