Science:Math Exam Resources/Courses/MATH103/April 2013/Question 05 (a)/Statement

Consider the iterated map $\displaystyle x_{t+1}=4x_{t}^{3}-12x_{t}^{2}+8x_{t}$. Calculate the steady states (fixed-points, equilibria) and mark them in the sketch below. Determine the stability of each equilibrium (explain analytically or graphically). Plot a cobweb starting with $\displaystyle x_{0}$ just above 2 (the point is indicated in the sketch).