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 measured 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.
P' = 0.1P(1- P/10) - 0.1
(b) Find and classify the equilibrium points for your model.
Equilibrium points: 1.12702 (asymptotically stable), 8.87298 (unstable)
(c) Use qualitative analysis to completely discuss the fate of the fish population with this model. In particular, if the initial fish population is 1000, what happens to the fish as time passes? What will happen to an initial population having 2000 fish?
With 1000 fish, the population will increase to 1.12K fish EQ point.
With 2000 fish, the population will decrease to the 1.12K fish EQ point.
I hope I did this correctly.
P' = 0.1P(1- P/10),
where time is measured 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.
P' = 0.1P(1- P/10) - 0.1
(b) Find and classify the equilibrium points for your model.
Equilibrium points: 1.12702 (asymptotically stable), 8.87298 (unstable)
(c) Use qualitative analysis to completely discuss the fate of the fish population with this model. In particular, if the initial fish population is 1000, what happens to the fish as time passes? What will happen to an initial population having 2000 fish?
With 1000 fish, the population will increase to 1.12K fish EQ point.
With 2000 fish, the population will decrease to the 1.12K fish EQ point.
I hope I did this correctly.