Case (ii)  If  [Graphics:Images/HarvestingModelMod_gr_168.gif] there are two stationary solutions  [Graphics:Images/HarvestingModelMod_gr_169.gif]  and  [Graphics:Images/HarvestingModelMod_gr_170.gif].

Example 9. Solve the population model with harvesting  [Graphics:Images/HarvestingModelMod_gr_171.gif],  
using the constants  a = 4,  b = 1,  and  k = 3,  and explore this situation.

Solution 9.

[Graphics:../Images/HarvestingModelMod_gr_172.gif]


[Graphics:../Images/HarvestingModelMod_gr_173.gif]

Construct the general solution.

[Graphics:../Images/HarvestingModelMod_gr_174.gif]



[Graphics:../Images/HarvestingModelMod_gr_175.gif]

Construct the constant solutions.  

[Graphics:../Images/HarvestingModelMod_gr_176.gif]


[Graphics:../Images/HarvestingModelMod_gr_177.gif]

 

 

Find  [Graphics:../Images/HarvestingModelMod_gr_178.gif].  

[Graphics:../Images/HarvestingModelMod_gr_179.gif]


[Graphics:../Images/HarvestingModelMod_gr_180.gif]

 

 

Remark.  Notice that  [Graphics:../Images/HarvestingModelMod_gr_181.gif]  tends to the second constant function  [Graphics:../Images/HarvestingModelMod_gr_182.gif]  as [Graphics:../Images/HarvestingModelMod_gr_183.gif].  
It will take more investigation to see what is happening.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004