提出动态协同新模型,揭示环境记忆如何影响群体行为稳定性。
Feedback-Coupled Memory Systems: A Dynamical Model for Adaptive Coordination
- 用环境记忆与激励反馈构建闭环动态系统,突破传统优化思路。
- 在耦合强度临界值β_c处出现纽马克-萨克尔分岔,预示协调崩溃。
- 适用于大规模群体(达10⁶人)和非线性场景,适合复杂系统研究者。
本文构建了一种称为反馈耦合记忆系统(FCMS)的动力学框架,用于描述多智能体系统的自适应协调机制。不同于传统的均衡优化或以个体为中心的学习,该模型将智能体、激励与持续环境之间的闭合回路互动形式化:环境存储累积的协调信号,分布式激励场局部传递这些信号,智能体据此更新行为,形成反馈驱动的动力系统。主要结论包括:第一,在耗散性条件下,系统存在有界正不变区域,确保动力学可行性,无需全局最优;第二,当激励依赖于环境记忆时,协调无法简化为静态优化问题;第三,系统需双向耦合——记忆依赖的激励影响智能体更新,而智能体行为又重塑环境状态。数值分析显示,在最小设定下,耦合强度临界阈值β_c处出现纽马克-萨克尔分岔,提供系统稳定性的边界。接近该阈值时,恢复时间发散、方差增大,可作为可观测时间序列中的协调崩溃预警信号。额外模拟验证了在非线性饱和下的鲁棒性,并支持扩展至最多N=10⁶智能体的规模,更具现实应用潜力。该框架为复杂系统中的协调提供了动力学视角,可拓展至多智能体系统、网络交互及宏观集体动力学。
原文摘要 · Abstract (English)
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 ($β_c$), 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.
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