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What is Chaos Synchronization?

Chaos Synchronization is best explained on the example of what we call identical synchronization.

nosynch

If two chaotic oscillators are uncoupled, then knowing what one oscillator does tells us little about the state of the other oscillator at that moment. The figure shows a numerical simulation of the intensity of two uncoupled chaotic lasers. Chaotic means that the intensity of the light emitted by each laser oscillates chaotically. In the figure we compare the output of two uncoupled such lasers. One which we call the transmitter and the other one, the receiver. On the left side we plot the intensity of both transmitter and receiver as time evolves. Clearly the oscillations of the two lasers seem rather uncorrelated. One can get an idea of this correlation by plotting the intensity of the transmitter versus the intensity of the receiver. This is shown on the right where we observe a tangle indicating the uncorrelated oscillation of the two laser.

It turns out that if one couples chaotic systems in a smart way, then it may happen that they 'lock'. They oscillate in exactly the same way. They are still chaotic, but knowing what the transmitter does allows us to say what the receiver does at the same moment and vice versa. Since both chaotic oscillators behave exactly the same, this type of synchronization is called identical synchronization.

synch

Here we show identical synchronization after coupling of our two lasers. This time the correlation plot shows a diagonal line. This means that when the transmitter has a certain intensity at a given moment, measured along the horizontal axis, the receiver has at that moment exactly the same intensity which is measured along the vertical axis. The line appears because we plot a point for each moment in time for the whole time shown on the left. If at some moment the two intensities were not equal, we would get deviations from the diagonal as for instance in the first figure.

If the two lasers are synchronized, we know on the receiving end what the transmitters intensity is (or should be); it is equal to the intensity we observe at the receiver. If we now modulate information bits onto the transmitter signal, then at the receiver side we observe a difference of the signal we obtain from the transmitter and the synchronized signal from our own receiver laser. This difference is exactly the information bit. By comparing the signal we get from the transmitter and the one we have from the receiver, we can decode this information. In this way we can use chaos synchronization to communicate using chaotic oscillators.