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News from ICTP 94 - Features - Chaos
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.