Michaelis-Menten Kinetics in a Chemostat

a

1.5

b

1.5

c

0.35

The concentration of an organism culture

(

X

1

)

grows in the presence of nutrient concentration

(

X

2

)

at a rate described by the Michaelis–Menten scheme. In dimensionless form the kinetic equations are:

X

1

'(t)=a

X

1

(t)

X

2

(t)/(1+

X

2

(t))-

X

1

(t)

,

X

2

'(t)=-

X

1

(t)

X

2

(t)/(1+

X

2

(t))+b

. The time evolution of the two concentrations is presented as a function of the growth constant

a

, the nutrient flux,

b

, and the initial concentration,

c

. The phase plane map of these equations is shown simultaneously.