17 citations · 23 across the 8 of their papers we have counts for
8 papers
Solution manifolds of differential systems with discrete state-dependent delays are almost graphs
Tibor Krisztin, Hans-Otto Walther
We show that for a system of differential equations with discrete state-dependent delays the solution manifold, on which…
Operon Dynamics with State Dependent Transcription and/or Translation Delays
Tomas Gedeon, Antony R. Humphries, Michael C. Mackey +3
Transcription and translation retrieve and operationalize gene encoded information in cells. These processes are not instantaneous and incur significant delays. In this paper we st…
A finite atlas for solution manifolds of differential systems with discrete state-dependent delays
Hans-Otto Walther
Let . Consider the delay differential equation for $g:(\mathbb{R}^n)^{\bf k}\su…
Autonomous linear neutral equations with bounded Borel functions as initial data
Hans-Otto Walther
For equations with the neutral term strictly delayed we construct the fundamental solution, derive a variation-of-constants formula for inhomogeneous equations, and prove growth es…
The impact on mathematics of the paper ''Oscillation and Chaos in Physiological Control Systems'' by Mackey and Glass in Science, 1977
Hans-Otto Walther
The note describes the role of the Mackey-Glass equation and of a similar equation due to Lasota in the study of nonlinear delay differential equations between 1977 and 2012, as fa…
Delay differential equations with differentiable solution operators on open domains in , and processes for Volterra integro-differential equations
Hans-Otto Walther
For autonomous delay differential equations we construct a continuous semiflow of continuously differentiable solution operators , , on open s…
Fréchet differentiability in Fréchet spaces, and differential equations with unbounded variable delay
Hans-Otto Walther
We introduce and discuss Fréchet differentiability for maps between Fréchet spaces. For delay differential equations we construct a continuous semiflow of continuous…
Response of an oscillatory differential delay equation to a single stimulus
Michael C. Mackey, Marta Tyran-Kaminska, Hans-Otto Walther
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We…