Feedback-Coupled Memory Systems: A Dynamical Model for Adaptive Coordination

TL;DR

This paper introduces Feedback-Coupled Memory Systems (FCMS), a dynamical model for adaptive coordination among agents that emphasizes feedback loops, environmental memory, and stability analysis, diverging from traditional equilibrium-focused approaches.

Contribution

The paper presents a novel dynamical framework for coordination that incorporates environmental memory and feedback, with analytical results on stability, bifurcations, and robustness for large-scale systems.

Findings

Bounded invariant region ensures viability regardless of optimality.

Coordination with environmental memory cannot be simplified to static optimization.

Identified a Neimark-Sacker bifurcation point indicating stability boundary.

Abstract

This paper develops a dynamical framework for adaptive coordination in systems of interacting agents referred to here as Feedback-Coupled Memory Systems (FCMS). Instead of framing coordination as equilibrium optimization or agent-centric learning, the model describes a closed-loop interaction between agents, incentives, and a persistent environment. The environment stores accumulated coordination signals, a distributed incentive field transmits them locally, and agents update in response, generating a feedback-driven dynamical system. Three main results are established. First, under dissipativity, the closed-loop system admits a bounded forward-invariant region, ensuring dynamical viability independently of global optimality. Second, when incentives depend on persistent environmental memory, coordination cannot be reduced to a static optimization problem. Third, within the FCMS class, coordination requires a bidirectional coupling in which memory-dependent incentives influence agent updates, while agent behavior reshapes the environmental state. Numerical analysis of a minimal specification identifies a Neimark-Sacker bifurcation at a critical coupling threshold ($\beta_c$), providing a stability boundary for the system. Near the bifurcation threshold, recovery time diverges and variance increases, yielding a computable early warning signature of coordination breakdown in observable time series. Additional simulations confirm robustness under nonlinear saturation and scalability to populations of up to $N = 10^{6}$ agents making it more relevant for real-world applications. The proposed framework offers a dynamical perspective on coordination in complex systems, with potential extensions to multi-agent systems, networked interactions, and macro-level collective dynamics.