Case (i) If   [Graphics:Images/HarvestingModelMod_gr_81.gif]  there is one stationary solution [Graphics:Images/HarvestingModelMod_gr_82.gif].

Example 3. Solve the population model with harvesting  [Graphics:Images/HarvestingModelMod_gr_83.gif],
using the constants  a = 2,  b = 1,  and  k = 1,  and explore this situation.

Solution 3.

[Graphics:../Images/HarvestingModelMod_gr_84.gif]


[Graphics:../Images/HarvestingModelMod_gr_85.gif]

Construct the general solution.

[Graphics:../Images/HarvestingModelMod_gr_86.gif]



[Graphics:../Images/HarvestingModelMod_gr_87.gif]

Construct the constant solution.  

[Graphics:../Images/HarvestingModelMod_gr_88.gif]



[Graphics:../Images/HarvestingModelMod_gr_89.gif]

Find the limit as [Graphics:../Images/HarvestingModelMod_gr_90.gif].  

[Graphics:../Images/HarvestingModelMod_gr_91.gif]


[Graphics:../Images/HarvestingModelMod_gr_92.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004