用延迟耦合系统建模符号与几何场的动态交互，保证稳定性和全局吸引子。
Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs
- 通过双场耦合的滞后微分方程描述符号与几何场的动态行为。
- 在耦合强度满足条件时，系统对任意延迟均保持全局稳定。
- 适用于需要强稳定性保障的智能体控制与认知建模场景。
我们描述了一个动力系统，其中符号场与几何场通过双线性希尔伯特-施密特核耦合。该系统由历史空间上的滞后泛函微分方程（RFDE）完全描述，且在利普希茨条件和小增益条件下成立。我们证明，在恒定输入下，该RFDE是适定的，并存在紧致全局吸引子。主要子系统（H_L, X_R, P），包含两个主场及一个执行场，只要场间耦合满足 $C_{\mathcal{K}}^2 < μ_Lμ_R$，即对任意延迟均全局稳定。此外，我们给出了满足主定理假设的设计规范。
原文摘要 · Abstract (English)
We describe a dynamical system in which a symbolic field is coupled to a geometric field via a bipartite Hilbert-Schmidt kernel. The system is fully described by a retarded functional differential equation (RFDE) on the history space, subject to Lipschitz and small gain conditions. We show that the RFDE is well-posed under constant input and that it admits a compact global attractor. The principal subsystem $(H_L, X_R, P)$, which is comprised of the two primary fields as well as an executive field, is shown to be globally stable independent of delay, provided that the interfield coupling satisfies $C_{\mathcal{K}}^2<μ_Lμ_R$. In addition, we describe design specifications that fulfill the hypotheses of the main Theorem.
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