Chaotic systems that stay in step.

Chaotic systems that stay in step

A chaotic system has such a high degree of unpredictability that it's hard to imagine how two identical but independent systems could ever be synchronized. For example, the wildly fluctuating voltages characteristic of chaotic electronic circuits could never stay in step. Even if both circuits started off under virtually the same conditions, the tiniest differences would quickly lead to voltage readings that don't match at all. But it may be possible to synchronize parts of certain chaotic systems, say Louis M. Pecora and Thomas L. Carroll of the Naval Research Laboratory in Washington, D.C. The trick is to link the two systems by passing a common signal between them in just the right way.

Pecora and Carroll start with a known chaotic system, in the form of either a set of mathematical equations or an electronic circuit. They devide the given system arbitrarily into two subsystems and make a duplicate of one of the subsystems. A signal from the original system replaces the missing section and drives the duplicated fragment.

Computer simulations show that under some conditions, the values of certain parameters evaluated for the truncated, duplicate system converge to the same values as evaluated for the other, even when they have different starting points. Experiments with electronic circuits produce similar results: The voltages fluctuate rapidly in both circuits but stay in step.

Pecora and Carroll have now identified specific criteria necessary for achieving synchronization, but many questions remain open. "There's lots to explore," Pecora says. "You can come up with many different possibilities."

The ability to design synchronized but chaotic systems could eventually lead to new schemes for encrypting messages to keep them secret. Already it is possible to conceive of having two remote systems that behave chaotically yet remain synchronized by way of a single linking signal. Pecora also suggests that the synchronization process may be a useful metaphor for some types of brain responses.