Consider a modified version of the logistic dynamical system xt + 1 = rxt (1 - xnt).

Question:

Consider a modified version of the logistic dynamical system xt + 1 = rxt (1 - xnt). For the following values of n,
a. Sketch the updating function with r = 2.
b. Find the equilibria.
c. Find the derivative of the updating function at the equilibria.
d. For what values of r is the x = 0 equilibrium stable? For what values of r is the positive equilibrium stable?
n = 3.