Deterministic Chaos

Synchronization of Chaotic Processes

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.

Return to Synchronization of Chaotic Processes.