Steady state bifurcations for a glycolysis model in biochemical reaction

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.