5 papers
Switching, Multiple Time-Scales and Geometric Blow-Up in a Low-Dimensional Gene Regulatory Network
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan
ODE-based models for gene regulatory networks (GRNs) can often be formulated as smooth singular perturbation problems with multiple small parameters, some of which are related to t…
A dynamical systems approach to WKB-methods: The eigenvalue problem for a single well potential
Kristian Uldall Kristiansen, Peter Szmolyan
In this paper, we revisit the eigenvalue problem of the one-dimensional Schr{ö}dinger equation for smooth single well potentials. In particular, we provide a new interpretation of…
A Multi-Parameter Singular Perturbation Analysis of the Robertson Model
Lukas Baumgartner, Peter Szmolyan
The Robertson model describing a chemical reaction involving three reactants is one of the classical examples of stiffness in ODEs. The stiffness is caused by the occurrence of thr…
Analytic weak-stable manifolds in unfoldings of saddle-nodes
Kristian Uldall Kristiansen, Peter Szmolyan
Any attracting, hyperbolic and proper node of a two-dimensional analytic vector-field has a unique strong-stable manifold. This manifold is analytic. The corresponding weak-stable…
Travelling Waves and Exponential Nonlinearities in the Zeldovich-Frank-Kamenetskii Equation
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan
We prove the existence of a family of travelling wave solutions in a variant of the , a reaction-diffusion equation which model…