The Spectrum of Delay Differential Equations with Multiple Hierarchical Large Delays

• Published in: arXiv.org
• Main Authors: Ruschel, Stefan, Yanchuk, Serhiy
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 17.12.2019
• Subjects: Asymptotic properties; Convergence; Delay; Destabilization; Differential equations; Eigenvalues; Evaporation; Rescaling; Spectra; Structural hierarchy

We prove that the spectrum of the linear delay differential equation \(x'(t)=A_{0}x(t)+A_{1}x(t-\tau_{1})+\ldots+A_{n}x(t-\tau_{n})\) with multiple hierarchical large delays \(1\ll\tau_{1}\ll\tau_{2}\ll\ldots\ll\tau_{n}\) splits into two distinct parts: the strong spectrum and the pseudo-contin...