Alja’afreh M. Mathematical modeling and computational methods for research of ergatic systems with dynamic protection

The purpose of dissertation was to increase the safety of ergatic systems with dynamic protection by assessing the best parameters for the developed mathematical models and improving the computational methods for their analysis. In the dissertation work the new scientific results are obtained, such as: – the modified mathematical model of ergatic systems with dynamic protection was developed; the method of a singular model analysis with an boundary layer received its further development by constructing and evaluating the accuracy of asymptotic solution for ergatic systems with dynamic protection; the computational method for the asymptotic solution of Cauchy problems with different types of singularities and non-stationary control parameters has been improved with estimation of the small perturbation parameter for different speeds of the harmful process; the method for analysis of protected systems` stability received its further development; the presence of unconstrained chaotic motions in a non-autonomous system near the periodic motion of a corresponding autonomous ergatic system with protection at convergence of their oscillation periods was revealed with the help of numerical experiment. The practical value of the results obtained is that the developed methods allow us to assess the state and parameters of technical systems with protection, that leads to a steady and rapid suppression of the local harmful factors at an affordable price. The presented methods are also used in educational process of Kharkiv National University of Radio Electronics.