Publications in Scientific Journals:
H. Taghvafard, H. Jardón-Kojakhmetov, P. Szmolyan, M. Cao:
"Geometric analysis of oscillations in the Frzilator model";
Journal of Mathematical Analysis and Applications,
online
(2021).
English abstract:
A biochemical oscillator model, describing developmental stage of myxobacteria, is analyzed mathematically. Observations from numerical simulations show that in a certain range of parameters, the corresponding system of ordinary differential equations displays stable and robust oscillations. In this work, we use geometric singular perturbation theory and blow-up method to prove the existence of a strongly attracting limit cycle. This cycle corresponds to a relaxation oscillation of an auxiliary system, whose singular perturbation nature originates from the small Michaelis-Menten constants of the biochemical model. In addition, we give a detailed description of the structure of the limit cycle, and the timescales along it.
Keywords:
Relaxation oscillations; Blow-up method; Geometric singular perturbation theory; Myxobacteria
"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)
http://dx.doi.org/10.1016/j.jmaa.2020.124725
Created from the Publication Database of the Vienna University of Technology.