Reentrant value fields as delayed coupled reaction-diffusion systems on finite graphs
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Abstract (arXiv)
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 (HL, XR, 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 CK2<μLμR. In addition, we describe design specifications that fulfill the hypotheses of the main Theorem.
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References · 12
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