On differential equations with state-dependent delay: The principles of linearized stability and instability revisited

Electronic Journal of Qualitative Theory of Differential Equations

Eugen Stumpf¹ 

[1] University of Hamburg, Department of Mathematics, Bundesstrasse 55, 20146 Hamburg, DE - Germany;

关键词: linearized stability;    linearized instability;    state-dependent delay;    stability analysis;    functional differential equation;   

DOI  :  10.14232/ejqtde.2016.1.81

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown