Asymptotic approach to the general modelling problem

The research is related to the various aspects of the general theory of the modelling and qualitative analysis in complex systems dynamics, that are generated by applied problems of engineering practice. The generalization of the reduction principle, the creation of efficient technology of modelling; the elaboration of regular manners for decomposition of original problem are main aims of the investigations, that are connected with general problems of analysis and synthesis. In this work the asymptotic approach is developed. It is special one, that is formed on the well-known stability postulate and singularity postulate. Here the united methodology is accepted, that is based on Lyapunov´s methods and Chetayev´s ideas (1936, 1957). Besides the original objects, the singularly perturbed ones are considered from uniform point of view. All systems are interpreted as the systems with nonregular parametric perturbations. Such natural extension of the statements of Chetayev and Kuzmin (1957) for parametric stability makes it possible to ascertain the close methodological connection between general problems of stability and modelling. And it enables to go to the modelling problem understanding that the singularly perturbed one may be solved by asymptotic technique combining the methods of perturbation theory and stability