You might want to look at the help screens below
for this module.
The screen below finds the equilibrium points for the model
r(p) = 0.5 + 0.0015 p - 0.000001166667 p (p - 500)
f(p) = r(p) p
p(n + 1) = f(p(n))
The following screens show how the TI-92 can find 2-cycle points for this model.
Notice that in the screens above we solve the equation
rather than the more natural equation
Of course, these two equations should be identical but for some reason the second one doesn't work on the TI-92. See the screen below.
The next screen evaluates the derivative of the function f(f(x)) at the point 1353.9692 which is one of the 2-cycle points.
Notice the derivative is less than one in absolute value, so this 2-cycle is attracting.
The next two screens look at an example with an initial population so high that the population drops below the "threshhold" and dies out.
