Simple visual example of the patterns that Chaos finds in complexity.
"Chaos" is used here as a term that refers to a variety of new methods for dealing with nonlinear interdependent systems. This class of complex systems, noted for sensitivity to small effects and seemingly erratic behavior, has been difficult to comprehend using traditional methods and conceptualizations. The methods of chaos have proven to be remarkably effective in revealing new forms of simplicity hidden within complexity. This in turn has led to new understandings of how such systems operate. Nonlinear systems phenomena are present in many fields Ð from physics, engineering and meteorology to medicine, psychology and economics. Consequently there are many opportunities for application of the methods of chaos.
Computing capability makes the new approaches possible. The methods of chaos focus on the geometry of behavior of a system as a whole and are computationally intensive. Underlying patterns of behavior are best revealed through the use of graphical representation of data. It is only with the availability of high speed processing and improved technologies for graphical display of data that it has become possible to explore a range of behavior of nonlinear systems sufficiently large to permit observation of patterns within complexity. The need for geometric approaches to such problems has been known for many years -- it was first demonstrated by Poincare in 1892 in his proof that the three-body problem could not be solved by linear or simple curve approximation methods. However, computational complexity of the problems prevented Poincare's methods from being widely applied until the advent of high performance computing.
As a field chaos is less than 30 years old, but its methods are now being applied to problems in many fields of science and engineering. For example, in physics chaos has been used to refine the understanding of planetary orbits, to reconceptualize quantum level processes, and to forecast the intensity of solar activity. In engineering, chaos has been used in the building of better digital filters, the control of sensitive mechanisms such as ink-jet printers and lasers, and to model the structural dynamics in such structures as buckling columns. In medicine it has been used to study cardiac arrhythmias, the efficiency of lung operations, EEG patterns in epilepsy, and patterns of disease communication. In psychology it has been used to study mood fluctuations, the operation of the olfactory lobe during perception, and patterns of innovation in organizations. In economics it is being used to find patterns and develop new types of econometric models for everything from the stock market to variations in cotton prices.
As an example of the multi-applicability of chaos research products, a research group at the University of Maryland is developing control methods for highly sensitive chaotic processes. The control methods are to be used in such diverse applications as laser control, arrhythmical cardiac tissue, buckling magnetoelastic ribbon, and, in conjunction with Oak Ridge National Laboratory, fluidized bed devices used in chemical and energy applications.
Because chaos is new, growing and deeply interdisciplinary, it benefits greatly from the emerging NREN services for access to remote systems, for sustaining collaborative research activities, and for initiating and maintaining scientific dialogue.