Smarter logistics

MATH202_Week5Lab

Bonus lab: Smarter logistics

Lab 5: Bonus Lab

Question 1:

Question 2:

P

Let

 = 0

Nkp-KP2 – Na

Kp2– NkP +Na = 0

Now P can be find by

P =

As ax2 + bx +c = 0

Now a = k

b = -Nk

And c = Na

Now by putting the values in the formula we get

P =

P =

P =

The possible point of equilibrium will be

P1 =  and P2 =

As shown in the graph, by fixing the values of a2 the values of a1 is unstable as well as the values of K are also unstable. P1 is a sink and p2  is a source.

Question 3:

P

Let b = 1 and if a= a2 what will happen to fish population for various initial conditions

In the given equation and the case, “b” is a parameter that controls the frequency of the harvesting period on the other hand “a” in the given expression represents the amplitude of the harvesting period. For the required expression, the max harvesting can be reach to “2a” and the minimum can be “0”.

In the above expression, when t=0 and b=1 then the sin (0) will be 0. Therefore, it is not logical for the population when

Initial population= 0


Figure 1: fish population for initial conditions

It can be seen from the graph that at the initial value of K, N and a the fish population decreases

Question 4:

The expression mentioned in the part two, when a= a2 the fish population the rapid decrease in the fish population occurred as shown in the figure


figure: fish population for various conditions

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