Asymptotic properties of the spectrum of neutral delay differential equations

Abstract

Spectral properties and transition to instability in neutral delay differential equations are investigated in the limit of large delay. An approximation of the upper boundary of stability is found and compared to an analytically derived exact stability boundary. The approximate and exact stability borders agree quite well for the large time delay, and the inclusion of a time-delayed velocity feedback improves this agreement for small delays. Theoretical results are complemented by a numerically computed spectrum of the corresponding characteristic equations.

arXiv comment14 pages, 6 figures

References in corpus (5)

• Control of unstable steady states by time-delayed feedback methods
• Refuting the odd number limitation of time-delayed feedback control
• Control of unstable steady states by extended time-delayed feedback
• Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes
• Stability domains for time-delay feedback control with latency