English
 
Privacy Policy Disclaimer
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT
Add to Basket
  Local TagsRelease HistoryDetailsSummary

Released
Journal Article

Absolute stability and absolute hyperbolicity in systems with discrete time-delays

Authors
/persons/resource/yanchuk

Yanchuk,  Serhiy
Potsdam Institute for Climate Impact Research;

Wolfrum,  Matthias
External Organizations;

Pereira,  Tiago
External Organizations;

Turaev,  Dmitry
External Organizations;

External Ressource
No external resources are shared
Fulltext (public)
There are no public fulltexts stored in PIKpublic
Supplementary Material (public)
There is no public supplementary material available
Citation

Yanchuk, S., Wolfrum, M., Pereira, T., Turaev, D. (2022): Absolute stability and absolute hyperbolicity in systems with discrete time-delays. - Journal of Differential Equations, 318, 323-343.
https://doi.org/10.1016/j.jde.2022.02.026


Cite as: https://publications.pik-potsdam.de/pubman/item/item_26836
Abstract
An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete time-delays. In the case of a single delay, the absolute stability is shown to be equivalent to asymptotic stability for sufficiently large delays. Similarly, for multiple delays, the absolute stability is equivalent to asymptotic stability for hierarchically large delays. Additionally, we give necessary and sufficient conditions for a linear DDE to be hyperbolic for all delays. The latter conditions are crucial for determining whether a system can have stabilizing or destabilizing bifurcations by varying time delays.