A stable attractor in chaos theory

Chaos theory

Chaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

 or biology

Biology

Biology is a natural science concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. Biology is a vast subject containing many subdivisions, topics, and disciplines...

 is an equilibrium state into which a system settles until disrupted by a change in the environment. The system then settles to a new attractor

Attractor

An attractor is a set towards which a dynamical system evolves over time. That is, points that get close enough to the attractor remain close even if slightly disturbed...

.

In cellular automata a transition from a chaotic phase to a stable attractor is called a solution.

Some mathematical functions may never converge to a solution, but may cycle endlessly in a stable way.

Leibnitz et al. have devised a network routing scheme on a stable attractor model developed to account for the response of Escherichia coli

Escherichia coli

Escherichia coli is a Gram-negative, rod-shaped bacterium that is commonly found in the lower intestine of warm-blooded organisms . Most E. coli strains are harmless, but some serotypes can cause serious food poisoning in humans, and are occasionally responsible for product recalls...

bacteria to variations in nutrient availability. Information about data paths (bandwidth, transit time) is used to determine a stable attractor and to find a new attractor if the network falters. The system is stable in noisy environments.