Deterministic Chaos

6.T. Synchronization of Chaotic Processes

Christian Hyugens discovered that pendulum clocks with the same length pendulua synchronize (well, anti-synchronize) when supported nearby one another.
Little surprise that periodic processes can synchronize, but what about chaotic processes?
The coupled map lattice model, a combination of logistic maps that can synchronize, even when chaotic.
Examples of synchronizing 10 coupled logistic maps with s = 3.9, as the coupling constant varies from 0 to 1.
Examples of synchronizing 10 coupled logistic maps with s = 3.99, as the coupling constant varies from 0 to 1.
Now we average the outputs of the logistic maps.
To look for synchronization, first we examine the IFS driven by averages of coupled logistic maps.
The driven IFS experiments suggest that for c near the middle ranges, the logistic maps synchronize. We investigate further using return maps.
Here is an application to secure communication.

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