Chaos. To engineers, it has meant that their systems were at risk, and they did their best to engineer chaos out of them.

“It used to be a nuisance. Engineers would avoid it at all costs,” said Steven H. Strogatz, Cornell University associate professor of theoretical and applied mechanics.

Not anymore. Strogatz is among a growing number of researchers who are finding real-world engineering uses of chaos – the seemingly random and unpredictable behavior of systems that are otherwise governed by precise mathematical laws.

“The new view is: Don’t avoid chaos.  Exploit it,” Strogatz said.

And that’s just what he’s trying to do. The Cornell mathematician is studying what he calls “the frontier” of chaos – new applications and uses of what used to be thought of as a pain in the experiment.

The popular notion that chaos can be used to predict complex systems has not been realized.

“It’s been a dream of chaos theory for many years to predict the stock market, politics and the weather, but that’s premature,” Strogatz said. “It can’t be done, at least not yet. We know in our hearts that the weather is chaotic, but it’s not proven. Stock performance, too. But we don’t understand those systems well enough; they are far more complex.”

Instead, Strogatz has a new grant to help determine how to use chaos in engineering. Author of the widely used college textbook Nonlinear Dynamics and Chaos (Addison Wesley, 1994) and instructor of the popular course, “Nonlinear Dynamics and Chaos” (otherwise known as the Cornell Chaos Course), Strogatz is investigating the use of chaos in lasers for private communications.

Strogatz and Henry Abarbanel, director of the Institute for Nonlinear Science at the University of California-San Diego, and Rajarshi Roy, professor of physics at the Georgia Institute of Technology, have a $1.07 million grant from the National Science Foundation to study lasers that have been deliberately driven into chaos, and to use that chaos in a new system for private communications.

Just as spies of old would stand by a waterfall or fountain so that their conversations could be masked, so could communications by other means be masked by interference. In the case of lasers, the key is to have the chaos in the transmitting laser and the receiver laser synchronized so that the chaotic mask, or interference, can be subtracted out. What’s left is the message. Such a technique could have applications for cellular communications, as well.

Strogatz and his colleagues were first to demonstrate, in 1993, that “synchronized chaos” could be used for private communications. Using electronic circuits, Strogatz, then at MIT, with Alan Oppenheim and his graduate student, Kevin Cuomo, built a circuit of “synchronized chaos” and showed how to use it for private communications.

It worked the same way: To send a secret message, one first masks it with much louder chaos, which sounds like static, and then transmits the combined chaos and message.  If the receiver can synchronize perfectly to just the chaotic part, then the chaos can be subtracted off at the receiver, thereby revealing the message.

Strogatz’s collaborators showed experimentally that such a system actually can be made to work, and together they published a paper in 1993 demonstrating the principle with an analytical explanation for it.

Another area that interests Strogatz is mutual synchronization in populations of rhythmic individuals, or oscillators. As an analogy, think of an audience at a concert or ballgame, where everyone starts clapping in unison, even though no one person is the leader.

First noted by Christiaan Huygens in 1665 when he realized two clocks hanging side by side had pendula that swung in rhythm, each somehow affecting the other, this synchronization occurs in many systems. Biology is full of examples: Crickets synchronize their chirping. Fireflies in Southeast Asia synchronize their flashes (the males light up in a group to attract mates). Pacemaker cells in the heart synchronize when to fire. Neural cells in the brain synchronize voltage fluctuations. Women roommates sometimes find that their menstrual cycles become synchronized after living together for months.

Strogatz has the job of formulating equations that serve as mathematical models for such different oscillations in nature that lead to synchronization. Another NSF grant he has received with biologist Tim Forrest, formerly of Cornell and now at the University of North Carolina-Asheville, is to study the choruses of snowy tree crickets, which are plentiful in Ithaca.

By playing tapes of chirping, “I’m going to try to mathematically characterize their response,” Strogatz said. “One cricket is hearing and adjusting to another. Does that explain what happens in a group? If we can make models of this, if we can predict group behavior, we will understand how a population of biological oscillations synchronize themselves.”

The crickets are a prototype for what happens in other parts of nature. If successful, these studies will be the first to show how synchronizing occurs with oscillators in a biological example.

Such mutual synchronization also occurs in arrays of superconducting devices, known as Josephson junctions. Strogatz helped determine how these nonidentical voltage oscillations fell into rhythm, by adapting a model originally proposed for biological oscillators. “There is a wonderful unity among all these different examples of synchronization,” Strogatz said. “At a mathematical level, they are all governed by the same principles.” The synchrony in circuits and lasers is similar to the synchrony of oscillations found in nature as well.

As for chaos, Strogatz is one member of Cornell’s College of Engineering who welcomes it. “Uses of chaos are on the frontier,” he said.