SCALE FACTORS FOR COLLECTIVE DESCRIPTION OF THE VARIOUS NATURE SELF-ORGANIZED SYSTEMS
The paper attempts to specify the contents of the level of symmetry principles introduced by E. Wigner. Analytic expressions are proposed to unite three levels of the hierarchy: the system - the sub-system - the extreme, which allows us to consider diverse systems of relationships of various scales as a construction having common connections. The simulations is made based on the previously proposed proto-structure which is represented on the numerical axis and is understood as a tool for analyzing self-organization processes (transition from one type of order to another one). In a system, the allowed states are formed with the help of a proto-structure and form separate levels. The most significant of them is the level of the order parameter. The connections between the positions of the order parameter and its subordinate characteristics, as identified for the system, extend over the subsystem and the extreme using scale factors that are constructed on the basis of structural considerations.The established connections can be verified through the example of the Solar system on the ecliptic plane. The relative angular momentum serves as the order parameter. Applicability of the identified connections for the planetary system and satellite sub-systems is demonstrated through the reference to the known relative characteristics of the planets and the Sun. In this case, the ratios of the masses of the planets and the sun are considered as scale factors. The hydrogen atom is treated as an extreme when using an additional scale factor represented by the force ratio in the hydrogen atom. The model data is consistent with observable inputs up to a tenth of a percent.