Modeling of processes of nonlinear dynamics of development of multi-component production enterprises

The published article proposes new economic and mathematical models of the dynamics of development of enterprises formed by several different industries. Each individual component of the enterprise is provided with separate resources and carries out its own production. The resources of each component of the enterprise expended in the production process are restored through the introduction of domestic investments. The developed models of multi-component enterprises are presented in the form of systems of coupled differential equations regarding production factors. Stationary solutions of these systems of equations correspond to the equilibrium states of operation of enterprises and represent. To calculate the limiting values of production factors, which are stationary solutions of systems of differential equations, corresponding systems of finite equations are obtained that describe the equilibrium state of enterprise operation. It is shown that the most efficient operation of the heterogeneous enterprises under consideration will be achieved only when the limiting values of production factors coincide with the values of the resources used, which correspond to the maximum profit values of each production component. This coincidence is achieved by a certain set of coefficients for the accumulation rates of domestic investment, for the calculation of which special formulas are obtained in the article. For a two-component manufacturing enterprise, models for calculating output, costs and profits were built for each component and for the entire enterprise. Numerical solutions of the corresponding system of differential equations are presented, on the basis of which integral curves for production factors, outputs and profits are constructed for each component of the enterprise and for the entire enterprise as a whole.