Determine the stability of equilibrium points to the lac operon equation using the method of linearization: 0.01 + X² 1+ X² -0.4X Plot the equation and calculate the derivatives at each equilibrium point. dX' dX
Determine the stability of equilibrium points to the lac operon equation using the method of linearization: 0.01 + X² 1+ X² -0.4X Plot the equation and calculate the derivatives at each equilibrium point. dX' dX
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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Transcribed Image Text:5. Determine the stability of equilibrium points to the lac operon equation using the method
of linearization:
0.01 + X²
1+X²
Plot the equation and calculate the derivatives at each equilibrium point.
X' =
-0.4X
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Step 1: Define the essential terms
VIEWStep 2: Plotting the graph f(X)
VIEWStep 3: Calculating the stability of the equilibrium points
VIEWStep 4: Caluculating the nature of the first equilibrium point
VIEWStep 5: Caluculating the nature of the second equilibrium point
VIEWStep 6: Caluculating the nature of the three equilibrium point
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