TO REDUCTION PRINCIPLE IN DYNAMICS OF COMPLEX NONLINEAR SYSTEMS
Lyudmila K. Kuzmina
The research is connected with the problems of mathematical modelling in dynamics of complex systems (theory and applications). The general methods of qualitative analysis, the application to the reduction problem in mechanics are developed. The elaborated asymptotic approach, based on Lyapunov’s methods, on Chetayev’s ideas, on structural perturbations methods, allows to reduce this problem to the solving problems with singular perturbations. Effective manners, the dissemination of reduction principle (well-known in stability theory) for general qualitative investigation problems are elaborated.