Emergence Conventional definition An emergent property is a property that a collection or complex system has, but which the indivi...
Emergence
Conventional definition
An emergent property is a property that a collection or complex system has, but which the individual parts do not have. A property of a system is emergent, if it is not a property of any fundamental element, and emergence is the appearance of emergent properties and structures on a higher level of organization or complexity.
Proposed definition
In a complex system, if the function of the sum of any individual quantity of the parts or any property of their individual interactions has a local maximum or minimum (so the sum is a non-monotonous function), the local maximum, or minimum appears as a new quality of the complex system what we call an emergent property. The definition makes emergent properties to be predictable and analyzable deductively.
Chaos
Conventional definition
A dynamical system is chaotic if its evolution is highly sensitive to initial conditions. The deterministic nature of these systems does not make them predictable.
Proposed definition
A complex system becomes chaotic when the energy potential valley of its equilibrium, the energy minimum reached in its balanced position becomes to be comparable to the energy of the individual interactions of the parts of the system. Chaos emerges when a system's minimum energy becomes a shallow valley compared to the bounding energy of the parts.
Strange attractor
Conventional definition
The attractor is a state, which a system tends to evolve from a wide variety of starting conditions. An attractor is strange if the dynamics of it are chaotic. Attractor in chaotic systems is a locally unstable yet globally stable structure, where nearby points of the system diverge from one another but do not depart from the attractor.
Proposed definition
The strange attractor is the emergent property of the chaotic system.
No comments