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Similarity and Analogousness in Dynamical Systems and Their Characteristic Features

Mathematical models describing technically oriented dynamical systems are generally rather complex. Very time-consuming interactive procedures have to be used when selecting the structure and parameters of the system. Direct enumeration of options using such procedures can be avoided by applying a number of means, in particular, dimension methods and similarity theory. The use of dimension and similarity theory along with the general qualitative analysis of the system can serve as an effective theoretical research method. At the same time, these theories are simple. Using dimension and similarity theory, it is possible to draw conclusions when considering phenomena that depend on a large number of parameters, but so that some of them become insignificant in certain cases. The combined method of using the theory of similarity, analogousness and methods developed by the authors for testing the drive model provides insight into its dynamics, controllability and other properties. The proposed approach is based on systematization and optimization