Chemical Oscillations in Enzyme Kinetics

The Higgins model is a two variable model in enzyme kinetics. In contrast with other popular simple dynamical models like the Lotka-Volterra model, the Higgins model shows steady states, damped oscillations and stable limit cycles. For these three dynamical behaviors, stability analysis yields expressions of the eigenvalues, which are easy to obtain either analytically or with the use of Mathematica. With these expressions we can find the boundaries between the three dynamical regions in parameter space and the bifurcation point. Also, we have compared the Higgins model with the other two variable models and find that the origin of the richer dynamical behavior of the Higgins model is due to the enzymatic step in the mechanism.