Adding chaos to achieve synchrony.

Most scientists and engineers view the erratic, unpredictable behavior of a chaotic system, and its sensitive dependence on initial conditions, as something to avoid. A new finding, however, suggests that a dash of chaos may be just the ingredient needed to bring a set of separate but identical oscillators into synchrony.

This startling conclusion stems from the work of two scientists at the Naval Research Laboratory (NRL) in Washington, D.C. -- Louis M. Pecora, whose theoretical work and numerical simulations unveiled the effect, and Thomas L. Carroll, who designed and constructed an electrical circuit to demonstrate the phenomenon. The circuit shows how the addition of a small chaotic component to a smoothly varying, regularly repeating input signal used to drive two separate oscillators helps the signal emanating from the oscillators fall into step. Without this chaotic component, the two oscillators would generate signals that are either fully in step or exactly out of step.

"This is a new area," Pecora says. "There has been very little work on using chaotic signals to drive nonlinear systems." In a sense, he adds, "we're using chaos to make things behave better."

In Carroll's electrical analog, as signal generator feeds a smoothly varying wave to a pair of separate but identical oscillator circuits. In response, each circuit generates a fluctuating signal that repeats itself at intervals twice as long as those in the input signal. Nonetheless, although both oscillators are driven by the same input signal, they themselves generate signals that aren't necessarily matched, or in phase. Indeed, repeated experiments show that the output signals end up in phase only about half the time. However, when a chaotic component is added to the input signal, two oscillators that start out of sync rapidly match their signals and remain in phase from then on. Theoretical work indicates that synchronization should occur for any number of oscillators.

While these findings suggest a novel method for synchronizing signals coming from arrays of generators, they may have biological implications as well. "Our results now give a very concrete reason for having chaotic driving signals in the body," Pecora says. "Things don't get out of sync this way, yet they still behave smoothly and very similarly to periodically driven systems," such as heartbeats.