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Qualitative analysis of the minimal Higgins model of glycolysisBrigita Ferčec,
Matej Mencinger,
Tatjana Petek,
Orhan Ozgur Aybar,
Ilknur Kusbeyzi Aybar, 2023, original scientific article
Abstract: Glycolysis, one of the leading metabolic pathways, involves many
different periodic oscillations emerging at positive steady states of
the biochemical models describing this essential process. One of
the models employing the molecular diffusion of intermediates is
the Higgins biochemical model to explain sustained oscillations. In
this paper, we investigate the center-focus problem for the minimal
Higgins model for general values of the model parameters with the
help of computational algebra. We demonstrate that the model
always has a stable focus point by finding a general form of the first
Lyapunov number. Then, varying two of the model parameters, we
obtain the first three coefficients of the period function for the stable focus point of the model and prove that the singular point is actually a bi-weak monodromic equilibrium point of type $[1, 2]$. Additionally, we prove that there are two (small) intervals for a chosen parameter $a > 0$ for which one critical period bifurcates from this singular point after small perturbations.
Keywords: biological processes, biochemical models, glycolysis
Published in DiRROS: 18.03.2024; Views: 90; Downloads: 44
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