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:

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 $P(S\rightarrow S'|E)$ 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 “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.

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

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. 8 (4): 757–775. doi:10.1007/s11047-008-9096-6. S2CID 2723451.