The Fate of Fish Population: Analyzing the Logistic Equation with Fishing

[rocomath]

Very confused!

Consider a lake that is stocked with walleye pike and that the population of pike is governed by the logistic equation:

P'=0.1P(1-P/10),

where time is measures in days and P in thousands of fish. Suppose that fishing is started in this lake and that 100 fish are removed each day.

a) Modify the logistic model to account for the fishing.

b) Find and classify the equilibrium points for your model.

c) Use qualitative analysis to completely discuss the fate of the fish population with this model. In particular, if the initial population is 1000, what happens to the fish as time passes? What will happen to an initial population having 2000 fish?

a) P'=0.1P(1-P/10)-0.1P

b) 0.1P(1-P/10)-0.1P -> -P^2/10, P=0 which is stable.

Correct so far? I think I may need a hint for (c).

 

[HallsofIvy]

Why "-0.1P"? Your problem says that "100 fish are removed each day". That has nothing to do with P. (Initially, P= 1000 and 100= 0.1(1000) but P does not STAY 1000 while the number of fish removes stays at 100.)

 

[rocomath]

Hey Ivy, thanks for your comment! I haven't forgotten about this post (been really busy). My exam is on Tuesday so I will come back to this problem maybe later today. I will continue working on it and let you know what I get.