# (Logistic growth with periodic harvesting) The equation dp

Chapter , Problem 2

(choose chapter or problem)

QUESTION:

(Logistic growth with periodic harvesting) The equation

$$\frac{d p}{d t}=k p\left(1-\frac{p}{N}\right)-a(1+\sin b t)$$

is a non-autonomous equation that considers periodic harvesting. What do the parameters $$a$$ and $$b$$ represent? Let $$b=1$$ . If $$a=a_1$$, What will happen to the fish population for various initial conditions?

QUESTION:

(Logistic growth with periodic harvesting) The equation

$$\frac{d p}{d t}=k p\left(1-\frac{p}{N}\right)-a(1+\sin b t)$$

is a non-autonomous equation that considers periodic harvesting. What do the parameters $$a$$ and $$b$$ represent? Let $$b=1$$ . If $$a=a_1$$, What will happen to the fish population for various initial conditions?

Step 1 of 3

Consider the given equation,

$$\frac{d P}{d t}=k P\left(1-\frac{P}{N}\right)-a(1+\sin (b t))$$

Consider the formula corresponding to the “Logistic Growth with Periodic Harvesting model” as,

$$\frac{d P}{d t}=k P\left(1-\frac{P}{N}\right)-h$$

Here, h is the number of fish harvested each year due to fishing, $$P(t)$$ is the fish population at any time $$t$$, $$k$$ is the growth rate, and $$N$$ is the carrying capacity.