Explorations with some sequences
1. x(n+1) = 3.2[x(n)][ 1 - x(n)]
Consider the behaviour of the sequence for various x(0). Use a spreadsheet to display a table and graph for a sufficient range of n.
In particular, investigate the behaviour of the sequence for x(0) in the range of x(0) = .6875.
2. Investigate this sequence for a range of x(0).
x(n+1) = 3.83[x(n)][ 1 - x(n)]
3. For 0 < A < 2 examine
for -1 < x(0) < 1