CONVERGENCE OF OPERATED DYNAMIC SYSTEMS

Elfimov Vladislav Sergeevich, Master’s degree student, National research Ogarev Mordovia State University (68 Bolshevistskaya street, Saransk, Russia), du@math.mrsu.ru
Shchennikov Aleksey Vladimirovich, Applicant, National research Ogarev Mordovia State University (68 Bolshevistskaya street, Saransk, Russia), du@math.mrsu.ru
Shchennikov Vladimir Nikolaevich, Doctor of physical and mathematical sciences, professor, sub-department of applied mathematics, differential equations and theoretical mechanics, Ogarev Mordovia State University (68 Bolshevistskaya street, Saransk, Russia), du@math.mrsu.ru

621.3.011.7:531.391:517.925.53

10.21685/2072-3040-2018-2-9

Background. It is well known that convergence of dynamic processes reflects the property of stability during steady-state motions. The property of convergence is of crucial importance in solving various problems in electrical engineering. It should also be noted that each dynamic system must be convergent. It should also be noted that each dynamic system in electrical engineering should possess such quality as convergence. In this paper, we study, in terms of convergence, linear, nonlinear and multivariable controlled dynamical systems that describe the linear, nonlinear, and multivariable electric circuits. When studying biomedical problems such systems are available as well. The mathematical models considered in the paper are systems of ordinary differential equations. The convergence here implies that the system of differential equations has a unique periodic solution, uniformly asymptotically stable in
general.
Materials and methods. The article presents ordinary differential equations, which are mathematical models of electric circuits. We use the first and second methods of Lyapunov transfer laws between states multienzyme complex disturbances.
Results. Main results of the article are to define the methods to be used to study the convergence of mathematical models described by linear, nonlinear and multivariable systems of ordinary differential equations. And in addition, new theorems about the convergence were substantiated.
Conclusions. The scientific results of the article develop the theory of electric circuits. A new theorem about the convergence is substantiated in terms of multivariable systems, describing the dynamic processes in medico-biological systems.

convergence, the operated dynamic system, asymptotic stability

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