Asymptotic properties of the spectrum of neutral delay differential equations

Details Asymptotic properties of the spectrum of neutral delay differential equations Asymptotic properties of the spectrum of neutral delay differential equations

2012-01-28

arxiv.org/abs/1201.5957v1

Dynamical Systems 24, 361-372 (2009)

Nonlinear Sciences

Chaotic Dynamics

14 pages, 6 figures

Scientific paper

10.1080/14689360902893285

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.

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