Lidiia Аfanasieva

The work is focused on solving a set of problems related to the functioning of the enterprise (firm) in a competitive market environment. The stability of the firm in market conditions is determined by the ability to optimally manage available resources, effective planning for timely promotion of new products, the ability to adequately respond to challenges posed by sudden changes in market conditions. An important factor in achieving economic stability of the enterprise is the presence of the internal concept of self-development, which combines two main functions - marketing and management system (management). In this article the methodology of economic and mathematical modeling of a market condition of firm as process of interaction of functions of marketing and management has received the further development. A model is proposed, which is built in line with the paradigm of economic synergetics and is a system of two nonlinear ordinary differential equations. It is proved that in this situation the classical linear principle of superposition loses its relevance and does not allow the application of the traditional apparatus of econometric analysis. Therefore, the most important for the implementation of the practice of economic forecasting is the construction of areas of stability of the equilibrium of the firm. According to the results of the study, the emphasis is placed on the need to develop criteria for the proximity of system parameters to the dangerous limits of loss of stability by the firm, during the transition through which the economic system changes its dynamic mode catastrophically. A key place in the work is given to determining the parameters of cyclic processes, indicating the amplitude, frequency and nature of the stability of periodic trajectories. The presented results of numerical modeling have practical value and can be used for the analysis and forecasting of parameters at separate stages of the corresponding periodic modes of functioning of the enterprises with various types of stability.