Intra System Links Dynamics as a Cause of Development Cyclicity: The Simplest Equations

The description of the systems dynamics whose behavior is determined by a large number of random parameters is relevant for many areas. At the same time, the identification of system-forming factors and intra-system connections is the most important task. To identify such a system, vertical and horizontal analysis of the data describing the system is necessary. The paper uses a simplified approach to the analysis of multidimensional random data. At the qualitative level, the possibility of analyzing the system dynamics based on changes in intra-system links is clearly shown. The system dynamics is described by the Ornstein-Uhlenbeck equation, which allows to obtain analytical solutions. The results of the theoretical analysis at the qualitative level are confirmed by the author's data obtained during the analysis of psycho diagnostic data of personal development during the crisis period. The approach allows one to visually assess trends in the system development, interpret the possibility of crisis phenomena in the system, show the cyclical nature of development, based on the inhomogeneity of changes in intra-system connections. The results obtained are a confirmation and demonstration of the universal principle of system integration and differentiation.