1. The model is planned to define population growth in a confined space. The excess of births on natural deaths causes a growth rate of a times the current number of individuals N. Competition for food causes deaths from starvation at a rate of bN^{2} . Use Stella to simulate the population growth assuming:
a. a = .05
b. b = .00001
c. N = 500 at time t=0
2. Suppose in problem 1 which a second species exists in the same space subject to a_{1} =.04, b_{1}=.000015, and N_{1} =1,000 at time t=0. However interspecies fighting causes deaths to both species at a rate which is .000001 times the product of their numbers (.000001NN_{1}). Extend the model and run Stella to plot the population dynamics for both species.
3. We reviewed a probable model for houses sold and air conditioners sold as follows:
H: Number of households
y: # of houses sold
x: # of air conditioners sold
dy/dt = k_{1} (H - y)
dx/dt = k_{2 }(y - x)
Suppose we wish to extend the model through considering the breakdown of air conditioners. Then a decay model, where it assumes the decay rate depends on current level needs to be added to the model to reduce the level x. Also suppose we no longer take the housing limit H to be fixed. We thus need to extend the model to include
dx/dt = k_{2} (y - x) - k_{3}x
dH/dt = k_{4}H
Draw the flow diagram, make the Stella model and experiment with different values of and H.
k_{1}, k_{2,} k_{3}, k_{4 }and H