Bifurcation analysis of an enzyme-catalyzed reaction–diffusion system

Abstract

In this paper, we concern about the dynamics of a diffusive enzyme-catalyzed system arising from glycolysis, describing a biochemical reaction in which a substrate is converted into a product with positive feedback and into a branched sink. The temporal and spatiotemporal dynamics of the system under homogeneous Neumann boundary conditions, are studied. Preliminary analysis on the local asymptotic stability and Hopf bifurcation of the spatially homogeneous model based on ordinary differential equation is presented. For the reaction–diffusion model, firstly the parameter regions for the stability or instability of the unique constant steady state are discussed. Finally, bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied. Numerical simulations are presented to verify and illustrate the theoretical results.