Some physical measurements are the average of the measurements of
microscopic quantities. |
Think of how the temperature of a bath is related to the energy of
the individual water molecules, for example. |
Suppose instead of the individual logistic maps
xit, we see only
their average value zt at each time step t, |
zt = (x1t + ...
+ xNt)/N |
We shall drive an IFS with the sequence of these averages |
z1, z2, z3, ... |
Though there are many possibilities, we consider only a
simple example: |
two logistic maps, both with s = 4. |
Here the coupling formula becomes |
x1t+1 | = | (1-c)L(x1t) +
cL(x2t) |
x2t+1 | = | (1-c)L(x2t) +
cL(x1t) |
|
We shall use driven IFS and return maps to discover some coupling values
where these two chaotic logistic maps synchronize. |