Steady state bifurcations for a glycolysis model in biochemical reaction. (April 2015)

• Record Type: Journal Article
• Authors: Wei, Meihua; Wu, Jianhua; Guo, Gaihui
• Is Part Of: Nonlinear analysis. Volume 22(2015)
• Page Start: 155
• Page End: 175
• Publication Date: 2015-04
• Subjects: Glycolysis model -- Turing's instability -- Steady state solutions -- Lyapunov–Schmidt procedure -- Normal form; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2014.08.003
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper, a two-species glycolysis model is investigated in which one species is substrate and the other is activator. A linear stability analysis shows that there is a critical value for the diffusion rate of the substrate above which the constant steady state solution is of Turing's instability. Next, the steady state bifurcations are analyzed not only from a simple eigenvalue, but more difficultly, from a double one. The theoretical results are confirmed by numerical simulations. Our main methods are based on bifurcation theory, Lyapunov–Schmidt technique and singularity theory.