| Full text | |
| Author(s): |
Yanchuk, Serhiy
;
Wolfrum, Matthias
;
Pereira, Tiago
;
Turaev, Dmitry
Total Authors: 4
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 318, p. 21-pg., 2022-05-05. |
| 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. (c) 2022 Elsevier Inc. All rights reserved. (AU) | |
| FAPESP's process: | 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry |
| Grantee: | Francisco Louzada Neto |
| Support Opportunities: | Research Grants - Research, Innovation and Dissemination Centers - RIDC |