Leírás
joint work with Masa Dukaric, Hassan Errami, Roman Jerala, Tina Lebar, Valery G. Romanovski, Andreas Weber about the manuscript: https://arxiv.org/abs/1809.08840
One 3D and two 6D models (ODEs with rational right hand sides) of repressilators have been introduced. All the models have a single positive stationary point which is locally asymptotically
stable. This framework is quite routine but to prove the steps are far from being trivial: polynomial varieties are used to determine the existence and uniqueness of the stationary points. The calculations also needed the use of Mathematica, Singular and QeHopf.
The existence of the stationary points in all the three cases can also be proven in the following way. One transforms the right hand side into a polynomial without negative cross-effect, then constructs a reversible reaction which induces the given right hand side, therefore the existence follows. (In other words: we apply a result from reaction kinetics in mathematics.)
2. The above lecturer also promised to present reviews on conferences. Now these can be found (in Hungarian) here:
http://www.ematlap.hu/index.php/hirek-ujdonsagok-2018-09/773-2018-a-matematikai-biologia-eve
http://www.ematlap.hu/index.php/gazda-g-sag-2018-09/774-30-eves-a-wolfram