The Static bifurcation Diagram for the Gray-Scott Model

Gray, Scott and their collaborators proposed the model analyzed in our paper in the 80’s. The model describes an autocatalytic mechanism in isothermal systems where the reaction rate is increased by strengthening the concentration of one of the products. The chemical reaction (Fig. 1) occurs in a continuously stirred tank reactor (CSTR) and it involves two reactants X and Y with concentrations x and y respectively. Y is produced both autocatalytically and by an uncatalyzed process and it degrades with first order kinetics. The corresponding mathematical model is the system of two first order ODEs  dx dt = k0(x0 − x)− k1xy − k3x ,