SPLITTING OF THE ALOWED STATES IN A COMPLEX SELF-ORGANIZED SYSTEM. PART I
The paper considers scenarios of node splitting in a complex self-organized system,where nodes are components of the spectrum of the allowed states. In application, this allows us to explain the formation of the characteristics of planetary orbits in the Solar system. The research tool is the previously proposed proto-structure understood as a primary system of relations, with the help of which situations are modeled on the numerical axis in the relative characteristics of objects of different nature. The proto-structure consists of a rigid and a soft component - numerical sequences, which, in their turn, consist of cycles, i.e. repeating sets of relations. The proto-structure is intended for a phased study of the evolution (deployment) of observed self-organized systems. On the basis of the rigid component of the proto-structure, an order parameter of the system is formed, which subordinates the other two relative characteristics. The paper explores the process of matching the two components of the proto-structure resulting in the nodes in one of its cycles being split and shifted. Each node is represented by a spectrum, i.e. a set of positions, and any of them is interpreted as a separate element of the order parameter n , to which one of the positions at the lower level of the hierarchy is subordinate. The stability of the spectrum is interpreted as a consequence of the identical coincidence of nodes that belong to different nodal configurations and are interpreted in a mutually exclusive way. The selection procedure for the coordination of nodal configurations is a search engine, has a geometric nature, takes into account the background, and models the natural selection process in the system. The instability analysis is carried out using a special technique. A detailed discussion of the deployment of the system is presented.The formation of the spatial structure of planetary orbits in the ecliptic plane of the Solar system is presented to show the applicability of the method. Initially, the role of the order parameter n is played by the relative angular momentum, which in the process of evolution is transformed into the spectrum of the order parameter n . The positions of the named spectrum define the perihelion, aphelion, and semi-axes of the planetary orbits. The deviation of model results from observational data by distance averages 0.06%.