41 citations · 64 across the 16 of their papers we have counts for
17 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 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…
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…
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…
A Skin Microbiome Model with AMP interactions and Analysis of Quasi-Stability vs Stability in Population Dynamics
Eléa Thibault Greugny, François Fages, Ovidiu Radulescu +2
The skin microbiome plays an important role in the maintenance of a healthy skin. It is an ecosystem, composed of several species, competing for resources and interacting with the…
Canards in a bottleneck
Annalisa Iuorio, Gaspard Jankowiak, Peter Szmolyan +1
In this paper we investigate the stationary profiles of a nonlinear Fokker-Planck equation with small diffusion and nonlinear in- and outflow boundary conditions. We consider corri…
A dynamical systems approach to WKB-methods: The simple turning point
K. Uldall Kristiansen, P. Szmolyan
In this paper, we revisit the classical linear turning point problem for the second order differential equation with for . Writte…
Qualitative dynamics of chemical reaction networks: an investigation using partial tropical equilibrations
Aurélien Desoeuvres, Peter Szmolyan, Ovidiu Radulescu
We discuss a method to describe the qualitative dynamics of chemical reaction networks in terms of symbolic dynamics. The method, that can be applied to mass-action reaction networ…
Long-time behaviour of a model for p62-ubiquitin aggregation in cellular autophagy
Julia Delacour, Christian Schmeiser, Peter Szmolyan
The qualitative behavior of a recently formulated ODE model for the dynamics of heterogenous aggregates is analyzed. Aggregates contain two types of particles, oligomers and cross-…
A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
Annalisa Iuorio, Gaspard Jankowiak, Peter Szmolyan +1
In this paper, we investigate the stationary profiles of a convection-diffusion model for unidirectional pedestrian flows in domains with a single entrance and exit. The inflow and…
Singularly Perturbed Oscillators with Exponential Nonlinearities
Samuel Jelbart, Kristian Uldall Kristiansen, Peter Szmolyan +1
Singular exponential nonlinearities of the form with small occur in many different applications. These terms have essential singularities for leading t…
Geometric analysis of Oscillations in the Frzilator model
Hadi Taghvafard, Hildeberto Jardon-Kojakhmetov, Peter Szmolyan +1
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of…
Relaxation oscillations in substrate-depletion oscillators close to the nonsmooth limit
Kristian Uldall Kristiansen, Peter Szmolyan
In this paper, we describe a novel type of relaxation oscillations occurring in a model of substrate-depletion oscillators. Using geometric singular perturbation theory, with blow-…
Singular perturbation analysis of a regularized MEMS model
Annalisa Iuorio, Nikola Popovic, Peter Szmolyan
Micro-Electro Mechanical Systems (MEMS) are defined as very small structures that combine electrical and mechanical components on a common substrate. Here, the electrostatic-elasti…
Geometry and numerical continuation of multiscale orbits in a nonconvex variational problem
Annalisa Iuorio, Christian Kuehn, Peter Szmolyan
We investigate a singularly perturbed, non-convex variational problem arising in materials science with a combination of geometrical and numerical methods. Our starting point is a…
Multiscale Geometry of the Olsen Model and Non-Classical Relaxation Oscillations
Christian Kuehn, Peter Szmolyan
We study the Olsen model for the peroxidase-oxidase reaction. The dynamics is analyzed using a geometric decomposition based upon multiple time scales. The Olsen model is four-dime…
The Lopatinski determinant of small shocks may vanish
Heinrich Freistuhler, Peter Szmolyan
The Kreiss-Majda Lopatinski determinant encodes a uniform stability property of shock wave solutions to hyperbolic systems of conservation laws in several space variables. This not…