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Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs
[Submitted on 5 May 2026 (v1), last revised 30 May 2026 (this ve · 2026-06-24 · via cs.AI updates on arXiv.org

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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 $C_{\mathcal{K}}^2<\mu_L\mu_R$. In addition, we describe design specifications that fulfill the hypotheses of the main Theorem.

Submission history

From: Karsten Bohlen [view email]
[v1] Tue, 5 May 2026 16:29:44 UTC (42 KB)
[v2] Fri, 8 May 2026 18:07:37 UTC (48 KB)
[v3] Wed, 20 May 2026 16:14:35 UTC (55 KB)
[v4] Sat, 30 May 2026 19:39:08 UTC (48 KB)