# Michaelis-Menten Kinetics in a Chemostat

Michaelis-Menten Kinetics in a Chemostat

The concentration of an organism culture grows in the presence of nutrient concentration at a rate described by the Michaelis–Menten scheme. In dimensionless form the kinetic equations are: , . The time evolution of the two concentrations is presented as a function of the growth constant , the nutrient flux, , and the initial concentration, . The phase plane map of these equations is shown simultaneously.

(X)

1

(X)

2

X'(t)=aX(t)X(t)/(1+X(t))-X(t)

1

1

2

2

1

X'(t)=-X(t)X(t)/(1+X(t))+b

2

1

2

2

a

b

c