View source for Adaptive system

{{Short description|System that can adapt to the environment}}
{{Refimprove|date=November 2008}}

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 system]]s that utilize [[negative feedback]] to maintain desired states.

==The law of adaptation==

The law of adaptation may be stated informally as: 
{{quote|Every adaptive system converges to a state in which all kind of stimulation ceases.<ref>José Antonio Martín H., Javier de Lope and Darío Maravall: "Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature" Natural Computing, December, 2009. Vol. 8(4), pp. 757-775. [https://dx.doi.org/10.1007/s11047-008-9096-6 doi]</ref>}}

Formally, the law can be defined as follows:

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

:<math>P(S \rightarrow S'|E)>P(S \rightarrow S') </math>

''Let <math>S</math> be an arbitrary system subject to changes in time <math>t</math> and let <math>E</math> be an arbitrary event that is a stimulus for the system <math>S</math>: we say that <math>S</math> is an adaptive system if and only if when t tends to infinity <math>(t\rightarrow \infty)</math> the probability that the system <math>S</math> change its behavior <math>(S\rightarrow S')</math> in a time step <math>t_0</math> given the event <math>E</math> is equal to the probability that the system change its behavior independently of the occurrence of the event <math>E</math>. In mathematical terms:''

#- <math> P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0 </math>
#- <math> \lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')</math>

Thus, for each instant <math>t</math> will exist a temporal interval <math>h</math> such that:

:<math> P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')</math>

==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 “[[edge of chaos|adaptation to the edge of chaos]]” or ability to avoid [[chaos theory|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.<ref>Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008</ref> Physicists have shown that [[adaptation]] to the [[edge of chaos]] occurs in almost all systems with [[feedback]].<ref>{{cite journal|last1=Wotherspoon|first1=T.|last2=Hubler|first2=A.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J Phys Chem A|volume=113|issue=1|pages=19–22|doi=10.1021/jp804420g|pmid=19072712|year=2009|bibcode=2009JPCA..113...19W}}</ref>

==See also==
{{Portal|Evolutionary biology}}
{{div col|colwidth=22em}}
* [[Autopoiesis]]
* [[Adaptive immune system]]
* [[Artificial neural network]]
* [[Complex adaptive system]]
* [[Diffusion of innovations]]
* [[Ecosystems]]
* [[Gaia hypothesis]]
* [[Gene expression programming]]
* [[Genetic algorithms]]
* [[Learning]]
* [[Neural adaptation]]
{{div col end}}

==Notes==
{{Reflist}}

==References==
* {{cite journal
  | last = Martin H. | first = Jose Antonio | author-link = Jose Antonio Martin H.
  | author2 = Javier de Lope
  | author2-link = Javier de Lope
  | author3 = Darío Maravall
  | author3-link = Darío Maravall
  | title = Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature
  | journal = Natural Computing
  | volume = 8 | issue = 4
  | pages = 757–775
  | date = 2009
  | doi  =  10.1007/s11047-008-9096-6 
| s2cid = 2723451 }}

==External links==
{{Wiktionary | anapoiesis}}
{{Wiktionary | practopoiesis}}
[[Category:Control engineering]]
[[Category:Organizational cybernetics]]