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.

Relaxation oscillations; Blow-up method; Geometric singular perturbation theory; Myxobacteria

"Official" electronic version of the publication (accessed through its Digital Object Identifier - DOI)

Created from the Publication Database of the Vienna University of Technology.