This is a collection of graphs of pseudo phase spaces for the logistic map for values of mu from 3.5 to 3.99 in steps of 0.01
The iteration started at x=.5, the first 1000 values where calculated, and the next 5000 values are displayed. The first 1000 vaules were not displayed as the logistic map takes some time to settle down.
For most of these values of mu, the graphs are chaotic. However, for some show periodic behaviour. The following values of mu show periodic behaviour:
mu = 3.5 to 3.54, 'period 4' (ie. x(n+4)= x(n))
mu = 3.63, 'period 6' (ie. x(n+6)= x(n))
mu = 3.78, 'period 5' (ie. x(n+5)= x(n))
mu = 3.83 and 3.84, 'period 3' (ie. x(n+3)= x(n))
The value mu = 3.85 shows a small deviation from 'period 3'. However the 50 interval limitation of this model make the identification of the actual period difficult. I hope to remedy this drawback in the future.