5 citations · 7 across the 4 of their papers we have counts for
6 papers
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-…
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-…
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…