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Concept
Adaptive system
Summary
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 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:
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.
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Complex system
A complex system is a system composed of many components which may interact with each other. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations (like cities), an ecosystem, a living cell, and ultimately the entire universe.
Self-organization
Self-organization, also called spontaneous order in the social sciences, is a process where some form of overall order arises from local interactions between parts of an initially disordered system. The process can be spontaneous when sufficient energy is available, not needing control by any external agent. It is often triggered by seemingly random fluctuations, amplified by positive feedback. The resulting organization is wholly decentralized, distributed over all the components of the system.
Feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to feed back into itself. The notion of cause-and-effect has to be handled carefully when applied to feedback systems: Simple causal reasoning about a feedback system is difficult because the first system influences the second and second system influences the first, leading to a circular argument.