Chemostat Model

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Chemostat Model
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dx/dt rate produced rate out dS/dt rate in
rate out rate consumed
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Assume g(S)mS/(aS), a Monod or Michaelis-Menton
saturation function, which means that the
organism is limited in its ability to consume
nutrient. m is the maximal growth rate (units
1/t) and a is the half-saturation constant (units
mass/vol).
g(a)m/2
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Model Analysis
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Model Analysis
When mgt1 and ?lt1, the equilibrium (0,1) is a
saddle and E(1-?,?) is globally stable. If m3
and a1 then E(.5,.5).
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Competition
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Competition
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Competition
?1.5, ?2.667
?1.5, ?2.4
x1, x2 on S
?1.5, ?2.5
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Prey-Predator
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Prey-Predator
a10.3
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References

• L. Edelstein-Kesket, Mathematical Models in
  Biology, Random House, New York, 1988.
• S.B. Hsu, S.P. Hubbell and P. Waltman, A
  mathematical theory for single nutrient
  competition in continuous cultures of
  micro-organisms, SIAM Jour. Appl. Math. 32,
  366-383, 1977.
• H.L. Smith and P. Waltman, The Theory of the
  Chemostat Dynamics of Microbial Competition,
  Cambridge University Press, 1995.