Adaptive system explained

An adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological homeostasis or evolutionary adaptation in biology. Feedback loops represent a key feature of adaptive systems, such as ecosystems and individual organisms; or in the human world, communities, organizations, and families. Adaptive systems can be organized into a hierarchy.

Artificial adaptive systems include robots with control systems that utilize negative feedback to maintain desired states.

The law of adaptation

The law of adaptation may be stated informally as:

Formally, the law can be defined as follows:

Given a system

S , we say that a physical event E is a stimulus for the system S if and only if the probability P(S → S'|E) that the system suffers a change or be perturbed (in its elements or in its processes) when the event E occurs is strictly greater than the prior probability that S suffers a change independently of E :P(S → S'|E)>P(S → S')

Let

S be an arbitrary system subject to changes in time t and let E be an arbitrary event that is a stimulus for the system S : we say that S is an adaptive system if and only if when t tends to infinity (t → inf ty) the probability that the system S change its behavior (S → S') in a time step t _{0} given the event E is equal to the probability that the system change its behavior independently of the occurrence of the event E . In mathematical terms:

1. -

P _{t _{0}} (S → S'|E) > P _{t _{0}} (S → S') > 0

1. -

\lim _{t →} P _{t(S →} S' | E) = P _{t(S →} S')

Thus, for each instant

t will exist a temporal interval h such that:P _{t+h} (S → S' | E) - P _{t+h} (S → S') < P _{t(S →} S' | E) - P _{t(S →} S')

Benefit of self-adjusting systems

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of self-adjusting systems is its “adaptation to the edge of chaos” or ability to avoid chaos. Practically speaking, by heading to the edge of chaos without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications.^[1] Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.^[2]

See also

• Autopoiesis
• Adaptive immune system
• Artificial neural network
• Complex adaptive system
• Diffusion of innovations
• Ecosystems
• Gaia hypothesis
• Gene expression programming
• Genetic algorithms
• Learning
• Neural adaptation

References

• Martin H. . Jose Antonio . Jose Antonio Martin H. . Javier de Lope . Javier de Lope . Darío Maravall . Darío Maravall . Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature . Natural Computing . 8 . 4 . 757–775 . 2009 . 10.1007/s11047-008-9096-6 . 2723451 .

Notes and References

1. Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008
2. Wotherspoon. T.. Hubler. A.. Adaptation to the edge of chaos with random-wavelet feedback. J Phys Chem A. 113. 1. 19–22. 10.1021/jp804420g. 19072712. 2009. 2009JPCA..113...19W.