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Information × Registration Number 0224U031865, 0122U201260 , R & D reports Title The development and application of mathematical methods to economics and technics in modern conditions popup.stage_title Head Maliarets Liudmyla M., д.е.н. Registration Date 26-06-2024 Organization Simon Kuznets Kharkiv National University of Economics popup.description2  Objects of the study are the technological process of continuous cultivation in a chemostatic installation of mixed microbiological cultures; a complex dynamic system, the elements of which have both positive and negative feedback. The purposes of the work are the quantitative analysis of dynamic models describing the production in continuous cultivators of mixed microbiological cultures with competitive and commensal interactions of species, which makes it possible to obtain optimal growing conditions and increase the efficiency of the system; analysis of the methodology of a construction of various types of models of the dynamics of the development of innovative processes, taking into account self-organization of the logistic type, which can take place both at the micro- and macro-levels, as well as the development of the theoretical foundations of the management of these processes. As a result of the research carried out, for the studied biological system the obtained result has been explained the stable coexistence of two competing species in the chemostat. Therefore, it can be concluded that under certain parameter values аnd initial conditions, it is possible to produce a mixed culture from two competing populations with a commensalism type of interaction; a qualitative analysis (by trajectories) of the innovation diffusion process was carried out and it was concluded that the presence of nonlinearity leads to fundamental changes in the behavior of the system depending on the direction and intensity of the controlling influence. The main results of the research are realized in the educational process of S. Kuznets KhNUE in the academic disciplines: “Higher Mathematics”, “Econometrics”, “Probability theory and mathematical statistics”. QUANTITATIVE ANALYSIS, MODELS OF LINEAR DYNAMICS, STEADY STATE, SYSTEM APPROACH, NONLINEAR DYNAMICS, FEEDBACK, PHASE SPACE, QUALITATIVE ANALYSIS BY TRAJECTORIES, ORDER PARAMETERS, BIFURCATIONS Product Description popup.authors Voronin Anatolii V. Lebedieva Iryna L. Maliarets Liudmyla M. Yaloveha Iryna H. popup.nrat_date 2024-06-26 Close