A SOFTWARE APPLICATION FOR THE ANALYSIS OF PHASE TRAJECTORY OF DYNAMIC SYSTEM WITH USING OF QUALITATIVE THEORY OF DYNAMICAL SYSTEMS(ON EXAMPLE OF THE ORGANIZATION IN THE MANAGEMENT OF HOUSING AND COMMUNAL SERVICES)

UDC 519.688: 332.87

А.А. Popov, А.О. Kuzmina

The purpose of the article is the enhancement of the instruments for automation of the qualitative research of the dynamic system and forecasting values of the parameters, which characterize organization activities in the economy (particularly in the field of management of housing and communal services). In this article, the problem of automation of the analysis of the phase trajectory of the dynamic system is solved (organization of management of housing and communal services), using the qualitative theory of dynamic systems. The research is relevant due to the insufficient level of automation of qualitative research of dynamic systems in the economy with the economic interpretation of research results. Methods of qualitative theory of dynamic systems, which are used, allow forecasting the state of the dynamic system without numerical simulation (for example, integrating differential system, which is a model of the dynamic system). In the article is presented technique, in accordance with research of the phase trajectory of the dynamic system using the software application, was conducted. Types of phase points in the phase plane in accordance with character of behavior of the phase trajectory plane in the neighborhood of the projection of the phase point were identified. By the example of the phase trajectory analysis, which characterizes activity of organization of management of housing and communal services, opportunities of the software application, building of projection of the phase trajectory into the three planes occurs. It was identified that in the phase planes equilibrium states as «stable node» and «stable focus» are missing, but there are equilibrium states such as «unstable node», «unstable focus» and «saddle». The example of detection of the «field of attraction» of the phase trajectory in phase plane is given. Types of «fields of attraction» were identified and economic interpretation for the «fields of attraction» was given. The main directions for the enhancement of the developed software application functionality are formulated. The materials of the article present the practical value for the experts, who are forecasting state of the organization in economy, and particularly in the housing and communal services.

Keywords: : organization, management, housing and utilities, software application, automation, forecasting, qualitative research, dynamic system, phase trajectory, phase point.

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