Каbalyants P. Mathematical modelling of network systems with singular equations of conditions

Mathematical models of impedance, admittance, transfer and hybrid engineering network, non-linear electrical networks and diversified economics are built in the dissertation. The models contain singular equations. Existence and uniqueness theorems for different classes of singular equations are obtained. The theoretical results are applied to the analysis of engineering networks, non-linear electrical networks and diversified economics. In particular, conditions of the existence of external pressures, which correspondents to a given external flows in engineering network, and conditions of the existence of output tensions and currents for given input tensions and currents of transfer non-linear electrical multipoles are received. For non-linear dynamical macroeconomics models conditions of the existence of production plans for fields, which satisfy given demands. A numerical experiment is realised for some constructed mathematical models.