It was found that complex and unpredictable results could be produced in the behavior of systems from entirely deterministic equations. Chaos, in the technical sense, should not therefore be seen, as in everyday language, as implying randomness, disorder and irregularity. In the zone between stability and instability, systems can be observed to demonstrate a general pattern of behavior even if their specific behavior is unpredictable.
Indeed Prigogine's dissipative structures can be seen as an example, from chemistry, of systems exhibiting chaotic behavior.
There is additional confusion surrounding the relationship between "chaos theory" and "complexity theory." Chaos theory was the first term to be used. It was employed to describe the similar results emerging from the study of chaotic behavior in different fields in the physical science. It is also, usually, the narrower in scope, referring to the mathematics of non-linear dynamic behavior in natural systems.
Complexity theory is wider in scope, used to describe the behavior over time of complex human and social, as well as natural, systems. The new name, complexity theory, reflects a recognition that complex social systems are able to change and evolve over time. They are not bound, therefore, by fixed rules of interaction and do not develop on the basis of the repetition of a mathematical algorithm.
Chaos theory concerns itself with "complexity adaptive systems" whereas the subject matter of complexity theory is "complex evolving systems." The Santa Fe Institute, established in 1984, is the best known research center specializing in the behavior of complex adaptive and complex evolving systems.
Gleick (1987) was able to claim that "20th century science will be remembered for three things: relativity, quantum mechanics and chaos."
Edward Lorenz's finding showed that tiny changes in a system's initial state do not inevitably lead to small-scale consequences. On the contrary, this "sensitive dependence on initial conditions" that complex systems exhibit means that minute changes can alter long term behavior very significantly. This is often referred to by commentators on chaos theory as the "butter-fly effect"; the idea being that the flapping of a single butterfly's wings, producing apparently insignificant changes in atmospheric conditions today, might have effects over time that would lead to a storm happening somewhere in the world that would not otherwise have happened, or vice versa.
A strange attractor seems to keep the trajectory followed by an otherwise unpredictable system within the bounds of a particular pattern. It keeps a system to a pattern without requiring it ever to exactly repeat itself. This can be distinguished from a "stable attractor", which demands it return to its original state. Strange attractors also produce "self-similar behavior", giving rise to the same pattern at whatever scale their effects are examined.
Exploration of the nature of self-similar behavior and "fractal" patterns has played an important role in the development of chaos and complexity theory.
(Jackson, 2000, Systems Approaches to Management. Kluwer Academic/Plenum Publishers. NY.)
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