“Two identical chaotic systems starting from almost identical initial states, end in completely uncorrelated trajectories. On the other hand, chaotic systems which are mutually coupled by some of their internal variables often synchronize to a collective dynamical behavior,” write Meital Zigzag at Bar-Ilan University in Israel and colleagues o the arXiv today.
And perhaps the most fascinating of these synchronized systems are those that show zero lag; that are perfectly synched. For example, in widely separated regions of the brain, zero lag synchronization of neural activity seems to be an important feature of the way we think.
This type of synchronization also turns out to be an important feature of chaotic communication. This is the process by which which information can be hidden in the evolution of a chaotic attractor and retrieved by substracting the same chaotic background to reveal the original message.
Obviously, this only works when the transmitter and receiver have are coupled so that they evolve in exactly the same way. For a long time physicists have wondered whether this effect can be used to send data securely and earlier this year, they proved that the security can only be guaranteed if the synchronisation has zero lag.
But how does zero lag occur and under what range of conditions?
Zero lag seems to occur when the delays in the mutual coupling and self feedback between two systems act to keep them in step. In effect, both systems lag but by exactly the same amount.
Until recently, this was thought to occur only for a very small subset of parameters in which the delays are identical or have a certain ratio. But these limits are so exact and constricting that it’s hard to imagine a wet system such as the brain ever achieving them.
Now Zigzag and friends have shown that it is possible to get around these strict limits by having more than one type of feedback between the systems. When that happens, it’s possible to have zero lag synchronisation over a much wider set of parameters.
That’s going to have important implications for our understanding of synchronisation in the brain and for the development of secure chaotic communication. Betcha!
Ref: arxiv.org/abs/0811.4066: Emergence of Zero-Lag Synchronization in Generic Mutually Coupled Chaotic Systems