This paper develops a dynamical theory of adaptive coordination governed by persistent environmental memory. Moving beyond framework-specific equilibrium optimization or agent-centric learning, I model agents, incentives, and the environment as a recursively closed feedback architecture: a persistent environment stores accumulated coordination signals, a distributed incentive field transmits them locally, and adaptive agents update in response. Coordination thus emerges as a structural consequence of dissipative balancing against reactive feedback, rather than the solution to a centralized objective. I establish three primary results. First, I show that under dissipativity, the closed-loop system admits a bounded forward-invariant region, ensuring viability independent of global optimality. Second, I demonstrate that when incentives hinge on persistent memory, coordination becomes irreducible to static optimization. Finally, I identify the essential structural condition for emergence: a bidirectional coupling where memory-dependent incentives drive agent updates, which in turn reshape the environmental state. Numerical verification identifies a Neimark-Sacker bifurcation at a critical coupling threshold ($β_c$), providing a rigorous stability boundary for the architecture. Results further confirm the framework's robustness under nonlinear saturation and demonstrate macroscopic scalability to populations of $N = 10^{6}$ agents.

翻译：本文发展了由持久环境记忆所驱动的自适应协调动力理论。超越特定框架的均衡优化或智能体中心学习范式，我将智能体、激励与环境建模为一个递归闭合的反馈架构：持久环境存储累积的协调信号，分布式激励场在局部传导这些信号，而自适应智能体则据此更新状态。因此，协调并非作为某个中心化目标的解涌现，而是作为反应性反馈下耗散平衡的结构性结果。我建立了三个主要结论。首先，我证明在耗散性条件下，闭环系统存在一个有界的前向不变区域，确保其在不依赖全局最优性的前提下具有生存能力。其次，我证明当激励依赖于持久记忆时，协调无法简化为静态优化。最后，我识别了涌现现象的必要结构条件：一种双向耦合，其中依赖记忆的激励驱动智能体更新，而智能体的更新又反过来重塑环境状态。数值验证在临界耦合阈值（$\beta_c$）处识别出一个奈马克-萨克分岔，为该架构提供了严格的稳定性边界。结果进一步证实了该框架在非线性饱和条件下的鲁棒性，并展示了其在宏观层面可扩展至包含$N = 10^{6}$个智能体的规模。