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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:
Every adaptive system converges to a state in which all kind of stimulation ceases.
Formally, the law can be defined as follows:
Given a system , we say that a physical event is a stimulus for the system if and only if the probability that the system suffers a change or be perturbed (in its elements or in its processes) when the event occurs is strictly greater than the prior probability that suffers a change independently of :
Let be an arbitrary system subject to changes in time and let be an arbitrary event that is a stimulus for the system : we say that is an adaptive system if and only if when t tends to infinity the probability that the system change its behavior in a time step given the event is equal to the probability that the system change its behavior independently of the occurrence of the event . In mathematical terms:
Thus, for each instant will exist a temporal interval such that:
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. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.
- ^ 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. doi
- ^ Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008
- ^ Wotherspoon, T.; Hubler, A. (2009). "Adaptation to the edge of chaos with random-wavelet feedback". J Phys Chem A. 113 (1): 19–22. Bibcode:2009JPCA..113...19W. doi:10.1021/jp804420g. PMID 19072712.
- Martin H., Jose Antonio; Javier de Lope; Darío Maravall (2009). "Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature". Natural Computing. 8 (4): 757–775. doi:10.1007/s11047-008-9096-6. S2CID 2723451.