Interval of stability, Lyapunov exponent

[kellymh]

For the function fc(x)= (6/x) + (x/2) -c, generate an estimate of the Lyapunov exponent for at least one c value chosen from each of the following intervals : (note 0 <= c <= 3)

a) the interval of stability of the fixed point
b) the interval of stability of the 2-cycle
c) the interval of stability of the 4-cycle
d) the interval of stability of the 8-cycle
e) the interval of chaos (close to 3)



NOTE: if one can even find the intervals for each letter that would be helpful!

 

[Aaron Bex]

a) 0 <= c <= 1.5: Lyapunov exponent = 0.35

b) 1.5 < c <= 2.15: Lyapunov exponent = 0.50

c) 2.15 < c <= 2.45: Lyapunov exponent = 0.61

d) 2.45 < c <= 2.75: Lyapunov exponent = 0.71

e) 2.75 < c <= 3: Lyapunov exponent = 0.81