Hans-Otto Walther

collaborators

3 papers

math.DS2025

Dynamics of a state-dependent delay-differential equation

Tomas Gedeon, Antony R. Humphries, Michael C. Mackey +2

We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model.…

math.DS2025

On Shilnikov's scenario with a homoclinic orbit in 3D

Hans-Otto Walther

The paper provides a detailed proof that complicated motion exists in Shilnikov's scenario of a smooth vectorfield $V$ on $ma t hbb R^{3}$ with $V (0) = 0$ so that the equation $x^{'} = V (x)$ …

math.DS2025

On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^{1}$

Hans-Otto Walther

Shilnikov's scenario in 3D consists of a vectorfield $V$ so that the equation $x^{'} (t) = V (x (t)) \in R^{3}$ with $V (0) = 0$ has a solution homoclinic to the origin and the eigen…

Dynamics of a state-dependent delay-differential equation

On Shilnikov's scenario with a homoclinic orbit in 3D

On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class C1

On Shilnikov's scenario in 3D: Topological chaos for vectorfields of class $C^{1}$