| 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. |