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Chaos theory

Chaos Theory is the popular name for the branch of mathematics, the physics and other sciences that deals with certain types of dynamic systems very sensitive to variations in initial conditions. Small variations in initial conditions can lead to such large differences in future behavior, complicating the long-term prediction. This happens even though these systems are in fact deterministic, i.e., its behavior can be completely determined knowing its initial conditions.

Classification

Dynamic systems can be classified basically into:

Stable

Unstable

Chaotic

A stable system tends over time to a point, or orbit, according to their dimension (attractor or sink). A system escapes from the unstable attractors. And a chaotic system manifests the two behaviors. On one hand there is an attractor by which the system is drawn, but simultaneously, there are "forces" that are far from it. Thus, the system remains confined in an area of ??state space, but without tending to a fixed attractor.

One of the major characteristics of an unstable system has a high dependence on initial conditions. In a system with known equations characteristics, and fixed initial conditions, one can know exactly its evolution over time. But in the case of chaotic systems, a slight difference in these conditions makes the system evolve quite differently. Examples of such systems include the solar system, the tectonic plates, the fluid in turbulent flow and the growth of population.

Complexity Theory

The term complexity theory may refer to:

The study of complex systems

The complexity theory of algorithms, an area of theoretical computer science to quantify the resources needed to solve a problem.

The algorithmic information theory: theory to describe and quantify the notion of complexity and content information of a data set, including the Kolmogorov complexity.

In most scenarios, required signal processing designs optimal result in a poor performance when conditions change scenario with time. Progress in better designs and its extreme dependence on the spectrum or the correlation signals to be treated, prevented requires the degradation of quality if the signals to be processed change their properties. Thus, when a signal processing system is able to adapt automatically signal environment, it is said that this is adaptive. A generic architecture adaptive system is a process step (usually a linear system) which is superimposed a learning structure. The observed learning structure and introduces conditions appropriate changes to the process system. What you see is but the digital version feedback systems in which analog, as being those which inspired these systems, recently led to encoding and decoding systems that act to limit next and are referred to as turbo-codes.

A complex adaptive system (CAS) is a special type of complex system , is complex in that it is diverse and consists of multiple interconnected elements, and adaptive, because it has the ability to change and learn from the experience.

The term "complex adaptive system” (or "science of complexity"), was coined at the interdisciplinary Santa Fe Institute by John H. Holland, Murray Gell-Mann and ...
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