4 papers · 1 filter
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 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…