Instructions for logistic time series program
This VB program produces times series and histograms for the
logistic function f(x)=ax(1-x) and the function g(x)=ax^2 sin(pi*x)
(see pages 616-617 of the text for the latter).
Begin by choosing one of those two functions (Function button
at the top).
Enter a value for a, initial point x_o,
and the number N of iterations.
Click on the Time Series button at the top to draw the
time series. You can plot up to 6 different time series on
one screen (changing any of the parameters). To see the histogram
of anyone of these time series, click on the Histogram
button at the top. You will be asked to choose which
plot (i.e., which time series) you would like converted into
a histogram (if you plotted 6 time series, they are numbered
1 to 3 across the top row from left to right, and 4 to 6
across the bottom row from left to right). Then you will
be asked for the number of bins. This is the number of
small intervals of [0,1], of equal size, that the computer
will use to group the points. The finest scale is
around 100 or so (depends on the size of your
screen, however bin sizes may affect the
appearance of the histogram even if it beyond the
resolution of your screen) while a coarse scale is around 50. Depending
on what features of the histogram you are looking for, you will
want to choose the number of bins accordingly.
Another button on the top is Difference. Here you will
be asked for two time series and the program will plot the
difference of the time series. You would use this feature when
studying the behavior of two time series with slightly
different initial points to observe the stability of
one of the orbits.
If you would like a larger plot of any of the time series, click on
the Zoom button. The button Function Graph
will draw the graphs of any iteration of the two
functions listed at the top (logistic and the other one).