Harman Patil (Editor)

Adaptive system

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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.

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

The law of adaptation

The law of adaptation can 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 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 ) 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
  2. - 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 “adaption 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 the feedback.

Practopoiesis

Practopoiesis, proposed as a term by one theorist, is a kind of adaptive or self-adjusting system in which autopoiesis of an organism or a cell occurs through allopoiesis among its components. The components are organized into a poietic hierarchy: one component creates another. For example, according to this proposal, in the brain this hierarchy leads to the capability of learning to learn.

References

Adaptive system Wikipedia