Dynamical Analysis of Michaelis-Menten Enzyme Reactions

Abstract

In this paper Michaelis-Menten type enzyme reactions are studied. With an output of this kind one could consider the following set of equations $\frac{dx}{d\tau }=a-bx-x^py^q$, $\frac{dy}{d\tau }=x^py^q-\frac{cy}{y+1} $. Taking some particular values of the parameters a, b, p, q  a detailed analysis of the system is taken up. The system is analysed by studying the associated differential equations, phase plane analysis and bifurcation analysis.