Year: 2026
Type: article
Abstract: We investigate the strong stability of linear neutral functional differential equations with multiple discrete delays, focusing on the existence of a uniform spectral gap separating the characteristic roots from the imaginary axis. We show that the loss of this spectral gap is governed by a structural dynamical mechanism: distinct coupling patterns in the characteristic determinant may generate identical frequency vectors, leading to cancellations through frequency collisions. Assuming rational independence of the delays, we lift the spectral problem to a multidimensional torus, where it can be interpreted in terms of frequency interactions on a compact dynamical system and analyzed via the combinatorics of the determinant expansion. This leads to the introduction of a graph-theoretic condition, called Pure Structural Injectivity (PSI), which prevents such collisions and depends only on the delay-labeled interaction graph. We prove that PSI is necessary for the existence of a uniform spectral gap, while under PSI and a standard contractivity condition the system admits a robust spectral gap. The framework extends to rationally dependent delays via invariant subtori, and in dimension three we provide a complete classification of structurally stable coupling patterns.
Author: Eric Dubon
Institution: University of Alicante
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Funder: Universidad de Alicante
OpenAlex ID: W7204457600