The Synchronization of Chaotic Systems

A system that is highly determined by its initial conditions, but whose outcome is unpredictable, is the idea behind chaos theory; it turns out even these systems can be synchronized.

Have you ever heard that when a butterfly flaps its wings in one part of the world, it can theoretically initiate a sequence of events that leads to the development of a hurricane in another part of the world? The butterfly effect, as it is called, is the concept that even small events can have large, widespread consequences.

As illustrated here, two chaotic systems, under the proper conditions, can be synchronized so that their signals are identical.
(Photo courtesy of Wikipedia)

For example, take a double pendulum and put it in motion. It will flip and turn in all kinds of random ways, but if you were to put it in motion again, would it follow the same trajectories? Probably not, because each time you put the pendulum in motion there will be minor changes to its starting position and that will change the trajectory outcome. This is the basic premise in the theory of chaotic systems.

In 1990, chaos was an intriguing type of motion. In theory, the motion of a chaotic system was completely determined by its starting conditions, but in practice chaos looked like random noise. Researchers at the Naval Research Laboratory were looking for a way to make this noise-like motion useful when they discovered a way to synchronize two remote chaotic systems. These two systems appeared to be generating random noise, but their motions were actually synchronized.

Chaotic synchronization has applications in secure communications, allowing a receiver to subtract transmitted chaos to reveal embedded signals. Other applications of chaos synchronization have gone far beyond those anticipated by the original researchers, leading to advances in understanding network nonlinear oscillators, and in fields as disparate as computer networks, coupled lasers, and networks of neurons in the brain.