Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs

arXiv:2605.03940v4 Announce Type: cross Abstract: 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_{K}^2<mu_Lmu_R. In addition, we describe design specifications that fulfill the hypotheses of the main Theorem.

Source: arXiv cs.AI | 2026-06-24