An increasing number of scientists are discovering that order has always been embedded within chaotic systems. We just haven't been able to uncover the underlying patterns--until now.

Chaos Rules

Chaos again took centre stage at ICTP this summer. But in typical ICTP fashion the event was meticulously organised.

The occasion for chaos's arrival was the Symposium on Synchronization of Chaotic Systems, which was held between 3-5 July 2000.

Hirokazu Fujisaka, Tomoji Yamada and Valentin Afraimovich launched the topic of synchronization of chaotic oscillators in the 1980s, but it only gained worldwide attention after Louis Pecora and Tom Carroll's hypothesis of its use for secure communications.

Later Kevin Cuomo and Alan Oppenheim showed that it was possible to encode messages within a noise-like chaotic signal. While this work raised hopes for a new system of secure communications, Gabriel A. Perez and Hilda Cerdeira at ICTP showed that the underlying structure of low-dimensional chaotic systems could be used by an eavesdropper to decode an encrypted message.

At the conference, more than 80 scientists from 27 countries listened to a broad range of presentations--25 in all--exploring the importance that the dimensionality of chaotic systems has in encrypting messages successfully.

What's so special about chaos and why does it deserve such extensive and careful examination? The short answer is this: Chaotic systems are unpredictable, unreliable and seemingly uncontrollable, but closer scientific and mathematical analyses often reveal that intricate, repetitive patterns lie behind the randomness. In other words, scientific studies can uncover the 'unseen' order in chaos and perhaps put that order to good use in areas ranging from communication technologies to genetic engineering to neural networks.

"One of the unique aspects of chaotic studies," explains Louis Pecora, conference organiser and staff scientist at the Naval Research Laboratory, in Washington, D.C., USA, "is that the field is truly multidisciplinary. At the conference, for example, Kunihiko Kaneko from the University of Tokyo, Japan, examined chaotic systems to better understand developmental cell biology and, more specifically, the intricately related physical and biochemical systems that enable lobsters to capture, chew and digest food. At the same time, José R. Rios Leite, from the Federal University of Pernambuco in Recife, Brazil, examined chaotic systems found in various light spectra to better understand the physics of lasers." As far apart as their research may seem, Kaneko and Rios Leite share the same methodologies in ways that allow them to learn from each other.

Thus, in a scientific world increasingly defined by narrower and narrower subfields, Pecora adds, the study of chaos stretches across many scientific disciplines.

What accounts for the cross-disciplinary nature of the study of chaos? Tito Arecchi, an Italian physicist at the University of Florence who was a speaker at the conference, observes: "This broad field is driven by a desire to find order in chaos by deciphering underlying patterns through, for example, mathematics or computer modelling."

"What scientists are trying to detect," he asserts, "are the repetitive signals that may be taking place within electric currents, light impulses or the microchemistry of organic molecules. These signals, if reduced to manageable levels of observation and analysis, can indeed turn chaos into order. The truth is that nature is brimming with regularity, most of which remains outside our purview."

"Another way of understanding the study of chaos," says Pecora, "is to view our analytical framework not as an abstract intellectual concept but as a universal tool that may prove useful in a variety of scientific disciplines. The problem is that the skills required to handle and apply the tool successfully remain difficult to master."

"A chaotic system contains one or more varying elements," Pecora notes. "These elements," he continues, "are in constant flux with patterns of motion that are not easy to pin down or replicate." As a result, scientists conducting research on chaotic systems must be prepared for constant surprises. In chaotic systems, unlike periodic systems, small changes grow exponentially--quickly leading to unpredictable changes and a loss of coherence. "All of this means that understanding how to synchronise chaotic systems may provide important insights in a variety of different fields, but the ability to do so is no simple task."

What is simple about chaos is the fact that you don't need complicated systems to create complex signals. This insight has served as the basis of one of the first real-world applications of the study of chaos: encryption.

"The simple signals that sound like background noise to those who don't know the code actually represent spoken words or written text to those who do," says Pecora. "By keeping a complex system simple, you make the decoding machinery both lighter and more resilient."

The roles that encryption could play in communications technologies are obvious, particularly in promoting the safe and secure transmission of information. Part of the aim of this meeting was to understand how simple the system can be to successfully encrypt undecodable messages.

Despite its seemingly exotic nature and its high-tech applications, the study of chaotic systems has not been confined to scientists in the developed world. The large number of Third World scientists who participated in the ICTP symposium (more than half of the total number) indicates that the study of chaos is not only multidisciplinary but multinational in nature.

"One reason for the involvement of scientists from the South in the study of chaos," notes Argentinean statistical physicist Damian H. Zanette, of Centro Atómico Bariloche, Bariloche, Argentina, "is that the amount of computing power a researcher needs to do good work is relatively small. As a result, overhead costs are cheap. This is one area of science where you don't need expensive equipment to keep pace with your colleagues."

Another reason Zanette cites is that several developing countries, among them Brazil, China and India, now have a critical mass of scientists who are well-educated and well-trained in disciplines that are driving 'chaos' research--notably mathematics and theoretical physics.

Finally, Zanette maintains that "the study of chaos is a relatively new field that has yet to create well-entrenched centres of excellence compared to those, for example, in high energy physics, which have been around for 30 years or more. Those with the talent and drive have an opportunity to leave their mark on the emerging field of chaos regardless of where they choose to pursue their research." At the conference, Zanette himself confirmed his assessment of the involvement of Third World scientists in the study of chaos by examining methodologies for its synchronisation.

The study of chaos, in short, is a truly global scientific enterprise that draws its strength and vitality largely from the universal language of mathematics. Whether encrypting or decoding communication systems, learning more about cell differentiation among living organisms, or probing the motion of electrons in advanced materials, the search for order within the 'veiled' chaos of our physical, chemical and biological worlds has captured the attention of scientists from many different disciplines and many different parts of the world. And like the chaotic systems they study, the knowledge that they uncover in the future promises to be both exciting and surprising.

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FIREFLIES AND BRAIN WAVES
As children, many of us would spend quiet evenings in late summer watching fireflies perform their flash dance in seemingly carefully choreographed harmony. Damian H. Zanette, a statistical physicist at Centro Atómico Bariloche, Bariloche, Argentina, has carried this childlike fascination into his professional life by applying his study of abstract mathematical models to, among other things, the mechanisms at work when certain fireflies synchronise their light signals.
"Those who study chaotic systems," he explains, "speak to each other through the common language of mathematics. Math enables physicists to speak to chemists, and chemists, in turn, to speak to biologists--despite the fact they are trained in different disciplines and often work in very different, seemingly unrelated, fields."
"Where studies of chaotic systems, and I might add nearly all other scientific studies based on mathematical models, have fallen short," Zanette says, "are in their inability to create a common language when it comes to describing natural phenomena. For example, when a biologist comes to me with a set of equations explaining his or her work, I can understand the math, but that knowledge does not necessarily help me, as a statistical physicist, to understand the actual phenomenon he or she is analysing--whether it's population dynamics or neurological disfunctions or biomolecular reactions."
That's the bridge that Zanette hopes to build in his research. "The models that I study describe synchronisation at an abstract level, but can be applied to biological populations such as fireflies to explain the mechanisms that allow them to blink in harmony. The models tell us that synchronisation is possible when communication within the population is long-range and when its effect on individual behaviour exceeds a certain threshold."
Such knowledge may not only help us understand the intriguing but perhaps trivial world of fireflies but may also shed light on such neurological disorders as epilepsy. During epileptic seizures, scientists have discovered that the brain's neural activities are completely synchronised (unlike the complex uncorrelated patterns displayed during normal brain functions).
By studying synchronisation models, scientists could conceivably help uncover mechanisms that would avoid the trauma of epilepsy. It's the peculiar link that synchronisation potentially provides between such diverse phenomena as the blinking of fireflies in a farm field and overcharged in-synch brain waves during epileptic seizures that make the study of the synchronisation of chaotic systems so fascinating to explore and so difficult to explain.

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