Deterministic Chaos

Synchronization of Chaotic Processes

To check the apparent synchronization suggested by the driven IFS, here we plot the return maps for the average of two logistic maps.

Recall the return map for a single logistic map is just the graph of the function y = L(x).

So when the return map of the average of two coupled maps is the graph of a logistic function, we have good evidence the functions have synchronized.

Note each is chaotic, exhibiting sensitivity to initial conditions, and we did not start them at the same x-value. Nevertheless, they synchronize in a range between about c = 0.3 and c = 0.7.

c=0.0
c=0.1
c=0.2
c=0.3
c=0.4
c=0.5
c=0.6
c=0.7
c=0.8
c=0.9
c=1.0
animate Click to repeat.

Return to Synchronization of Chaotic Processes.