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.

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.^[1]

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 $P(S\rightarrow S'|E)$ 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 $E$:

$P(S\rightarrow S'|E)>P(S\rightarrow S')$

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 $(t\rightarrow \infty )$ the probability that the system $S$ change its behavior $(S\rightarrow S')$ 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. - $P_{{t_{0}}}(S\rightarrow S'|E)>P_{{t_{0}}}(S\rightarrow S')>0$
2. - $\lim _{{t\rightarrow \infty }}P_{t}(S\rightarrow S'|E)=P_{t}(S\rightarrow S')$

Thus, for each instant $t$ will exist a temporal interval $h$ such that:

$P_{{t+h}}(S\rightarrow S'|E)-P_{{t+h}}(S\rightarrow S')<P_{t}(S\rightarrow S'|E)-P_{t}(S\rightarrow S')$

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.^[2]

See also

• Adaptive immune system
• Artificial neural network
• Complex adaptive system
• Diffusion of innovations
• Ecosystems
• Gene expression programming
• Genetic algorithms
• Learning
• Neural adaptation

Notes

1. 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
2. Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008

References

• 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. Springer. 8(4): 757–775. doi:10.1007/s11047-008-9096-6.

External links

• Practopoiesis offers solutions to nine long-standing problems in neuroscience and philosophy of mind