Synchronization of Chaos

The Dutch scientist Christiaan Huygens famously observed in 1665 that two pendulum-clocks situated in the same room would, over time, come to be synchronized. The explanation? The two clocks were actually interacting very weakly through movements of the floor. Even though each clock had its own distinct periodic frequency, the subtle interaction mediated by the floor brought their movements together. From a modern mathematical perspective, the phenomenon Huygens discovered is no longer surprising, as we know of many other systems – and many far more complicated than a pair of clocks – which exhibit the same kind of spontaneous synchronization. Examples range from the clapping hands of people in an audience to coupled superconductors or brain cells.

But all these examples involve naturally periodic elements. Natural synchronization seems much more surprising for inherently unstable chaotic systems, in which nearby trajectories move apart exponentially fast. As of the mid-1980s, in fact, most researchers thought that weak coupling between such systems would be unlikely to cause synchronization. Yet the phenomenon has turned out to be quite natural. In a recent book chapter, LML Fellow Jeroen Lamb and co-authors Deniz Eroglu and Tiago Pereira of the University of São Paolo in Brazil, reviewed recent progress in this area, and linked it up with the history of the field, especially the period of rapid advance since 1980. Lamb and colleagues cover basic theoretical topics and also review progress in using the synchronization of chaotic systems in applications such as secure communications, not only between two points but within complex networks of communicating elements. As the review makes clear, the field remains full of puzzles and fruitful avenues for further advancement.

The paper is available at https://arxiv.org/pdf/1703.08296.pdf

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