On differential equations with state-dependent delay the principles of linearized stability and instability revisited /
This paper deals with a dynamical systems approach for studying nonlinear autonomous differential equations with bounded state-dependent delay. Starting with the semiflow generated by solutions of such an equation, we revisit the principles of linearized stability and instability enabling the local...
Elmentve itt :
| Szerző: | |
|---|---|
| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2016
|
| Sorozat: | Electronic journal of qualitative theory of differential equations : special edition
2 No. 81 |
| Kulcsszavak: | Differenciálegyenlet - késleltetett |
| doi: | 10.14232/ejqtde.2016.1.81 |
| Online Access: | http://acta.bibl.u-szeged.hu/73748 |
| Tartalmi kivonat: | This paper deals with a dynamical systems approach for studying nonlinear autonomous differential equations with bounded state-dependent delay. Starting with the semiflow generated by solutions of such an equation, we revisit the principles of linearized stability and instability enabling the local stability analysis of equilibria via linearization. In particular, we prove both principles in an elementary way by using only a quantitative version of continuous dependence of the semiflow on initial data together with basic properties of the discrete semi-dynamical system induced by iterations of some time-t-map. |
|---|---|
| Terjedelem/Fizikai jellemzők: | 17 |
| ISSN: | 1417-3875 |