Consider the following graph of a first order nonlinear difference equation, in which the blue line corresponds to (), while the red line corresponds to the identity function = . Based on the above, determine the following:

a) Fixed points

b) Consider the following 4 initial values. For each of them sketch the evolution of the system in the phase diagram ().

0 = 1.2

0 = 0.5

0 = 0.5

0 = 1.2

c) Using the same initial values, sketch the phase diagram .

c) Based on the two previous diagrams, classify the fixed points of the system. Justify your answer.

f(x) 2 1 0 Xt 1.5 -1.5 -1 -05 0.5 1 0 -1 -2 -3 -4 -5