Investigating Long-Term Effects of Insect Poisioning on Bat Populations

[onie mti]

I am given
X^= ax -bxy-mx^2-p
Y^=cxy-dy
The insect population is measured in tons and the bat population in hundredss. The term -p reflects poisoning by farmers. The IVP are x(0) =40 and y(0)=1 the question is whether the poisinoning of the insects serves a purpose in the long run.

I let p=0 and was able to find my equilibrium points and drew my tanget curves now I am confused

 

[gtoguy97]

as to how to answer the question whether the poisinoning of the insects serves a purpose in the long run.The answer to your question depends on the context and what you are trying to achieve with the poisoning of the insects. If the goal is to decrease the insect population, then the poisoning may serve a purpose in the long run if the equilibrium points are such that the insect population decreases over time. However, if the equilibrium points are such that the insect population increases over time, then the poisoning may not be serving a purpose in the long run.