Feedback-Coupled Memory Systems in Continuous Time

Abstract

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 $\hat{I}¨$ - 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 $\hat{I}¨$ 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 $\hat{I}{\pm }_c=1/K$, 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.

19 pages, 4 figures. Extends arXiv:2603.11560 to continuous time. Code: github.com/stevefatz95/fcms-continuous