Английская Википедия:Adaptive system
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: Шаблон:Quote
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 “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
Notes
References
External links
Шаблон:Wiktionary Шаблон:Wiktionary
- ↑ Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008
- ↑ Шаблон:Cite journal
