DYNAMICS
| Collection | International Encyclopedia of Systems and Cybernetics |
|---|---|
| Year | 2004 |
| Vol. (num.) | 2(1) |
| ID | ◀ 992 ▶ |
| Object type | General information |
Classical dynamics was basically deterministic, in accordance — with linear causality, connecting variance of only one cause with the corresponding variance of one specific effect.
However, as stated by Y. SINAI, it became necessary to understand the conditions and ways by which “… a deterministic dynamics leads to the appearance of statistical laws… Secondly, why are statistical laws stable, i.e., why are they not destroyed by small noises, fluctuations, etc.? It has been believed for a long time that the appearance of statistical laws in dynamic systems was unavoidedly connected with the increase of the number of degrees of freedom allowing for corresponding averages. It is now clear that… in important classes of dynamic systems with few degrees of freedom, or even only two, a strictly deterministic dynamics leads to the appearance of statistical laws” (1992, p.70).
This understanding led to the study of ergodicity and, later on, to research into the onset of chaos and chaotic determinism. See: “Chaos (Onset of)”.
From another viewpoint, dynamics does not necessarily implies continuity, at least in models. Until now, we have no way to decide about dominance of continuity or discontinuity in the real world.
A.G. BARTO writes: “The term ”dynamic“ was originally associated only with continuous-time models since the differential equation was the only formalism available for modelling processes which unfold in time. We now know that the idea of dynamics is more general than the differential equation” (1978, p.167).
It is indeed now possible to spread out automata's dynamics through discrete models, as seen for example in CONWAY's “games of life”, which are easily modelled on digital computers.