Evaluate the population model where individuals emigrate when population is over

Question

Evaluate the population model where individuals emigrate when population is overly crowded. h individuals leave if pop. is larger than some critical value Nc.

N(t+1) = {rNt - h if Nt > Nc or rNt if Nt </= Nc}

a. Suppose h= 1000 Nc=1000 and r=1.5. Investigate some solutions starting with different values of N0 < 1000. What is happening?

b. Find equilibrium when h= 1000 Nc=1000 and r=1.5. What would happen to solutions starting with values greater than equilibrium? Use this info to sketch a cobweb diagram.

PLEASE SHOW ALL WORK TO GET POINTS

Explanation / Answer

1) When N0<1000,

N1=1000*N0

we check for

N0=100, N1=150

N0=500, N1=750

N0=800, N1=1200

So the population model does not hold as we see that population in third case exceeds threshold of 1000

2)equilibrium is 572

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