Suppose that we use K(C) = k C (for some constant k) instead of a Michaelis-Menten growth rate, in the chemostat model. (a) Find a change of variables so that only one parameter remains. (b) Find the steady state(s). Express it (them) in terms of the original parameters. Determine conditions on parameters so that a positive steady state exists, and explain intuitively why these conditions make sense. (c) Compare the conditions you just obtained with the ones that we got in the MM case. (d) Determine the stability of the positive steady state, if it exists
Suppose that we use K(C) = k C (for some constant k) instead of a Michaelis-Menten growth rate, in the chemostat model. (a) Find a change of variables so that only one parameter remains. (b) Find the steady state(s). Express it (them) in terms of the original parameters. Determine conditions on parameters so that a positive steady state exists, and explain intuitively why these conditions make sense. (c) Compare the conditions you just obtained with the ones that we got in the MM case. (d) Determine the stability of the positive steady state, if it exists
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that we use K(C) = k C (for some constant k) instead of a Michaelis-Menten growth rate, in the chemostat model.
(a) Find a change of variables so that only one parameter remains.
(b) Find the steady state(s). Express it (them) in terms of the original parameters. Determine conditions on parameters so that a positive steady state exists, and explain intuitively why these conditions make sense.
(c) Compare the conditions you just obtained with the ones that we got in the MM case.
(d) Determine the stability of the positive steady state, if it exists
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