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In the logistic model, N = 0 is a stable equilibrium point when ... а. r>0 O b. K>0 Ос r not equal to 0 С. O d. r<0

In the logistic model, N = 0 is a stable equilibrium point when ... а. r>0 O b. K>0 Ос r not equal to 0 С. O d. r<0

Advanced Engineering Mathematics
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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In the logistic model, N = 0 is a stable equilibrium point when... O a. r>0 O b. K>0 Ос С. r not equal to 0 O d. r<0
Transcribed Image Text:In the logistic model, N = 0 is a stable equilibrium point when... O a. r>0 O b. K>0 Ос С. r not equal to 0 O d. r<0
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The equilibrium point of a differential equation is the point where the rate of change is zero. For the differential equation dydx=fx, the equilibrium point is determined by solving the equation fx=0. Let the equilibrium point be x=x'. If f'x'<0, x=x' is stable. The negative sign of f'x' implies instability. When it equals zero, the equilibrium point is neutral. The logistic equation is one of the important differential equations having order 1. The population of a certain area is modeled through this equation. 

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