Bogdanov–Takens bifurcation of an enzyme-catalyzed reaction model

Enzyme-catalyzed reactions are frequently observed in the chemical process, and could be described by the mathematical model, such as the Gray–Scott model with Langmuir–Hinshelwood mechanism. The complex dynamical behaviors are analyzed in this work, including the existence and their stability of equilibrium points and the bifurcations of the model. By using stability theory, normal form technique and bifurcation analysis, the stability and the saddle-node bifurcation, Hopf bifurcation and Bogdanov–Takens bifurcation are explored in detail. Numerical simulations are also carried out to verify the validity of theoretical results.