Editing 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>
== Practopoietic theory ==
According to [[practopoietic theory]], creation of adaptive behavior involves special, ''poietic'' interactions among different levels of system organization. These interactions are described on the basis of [[cybernetic]] theory in particular, [[good regulator]] theorem. In practopoietic systems, lower levels of organization determine the properties of higher levels of organization, but not the other way around. This ensures that lower levels of organization (e.g., genes) always possess cybernetically more general knowledge than the higher levels of organization—knowledge at a higher level being a special case of the knowledge at the lower level. At the highest level of organization lies the overt behavior. Cognitive operations lay in the middle parts of that hierarchy, above genes and below behavior. For behavior to be adaptive, at least three adaptive traverses are needed.<ref name=Nikolic2014>{{Cite journal | doi=10.1016/j.jtbi.2015.03.003| title=Practopoiesis: Or how life fosters a mind| year=2015| last1=Nikolić| first1=Danko| journal=Journal of Theoretical Biology| volume=373| pages=40–61| pmid=25791287 |arxiv=1402.5332| bibcode=2015JThBi.373...40N| s2cid=12680941}}</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]]