4 papers
On a delay differential equation arising from a car-following model: Wavefront solutions with constant-speed and their stability
Eugen Stumpf
This work is concerned with the study of a scalar delay differential equation \begin{equation*} z^{\prime\prime}(t)=h^2\,V(z(t-1)-z(t))+h\,z^\prime(t) \end{equation*} motivated by…
Multiple slowly oscillating periodic solutions for x'(t) = f(x(t-1)) with negative feedback
Benjamin Kennedy, Eugen Stumpf
We consider the prototype equation x'(t) = f(x(t-1)) for delayed negative feedback. We review known results on uniqueness and nonuniqueness of slowly oscillating periodic solutions…
A note on local center manifolds for differential equations with state-dependent delay
Eugen Stumpf
In this note we consider local invariant manifolds of functional differential equations representing differential equations with state-dependent delay. Starting with a local center…
Local stability analysis of differential equations with state-dependent delay
Eugen Stumpf
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions…