Resumen
The subject of this work is the problem of the dynamic interaction of innovative products in a competitive market. Sustainable economic growth is currently impossible without increasing the competitiveness of enterprises and industries, largely determined by the strengthening of the competitive environment. As a result of the competition of economic agents for achieving various advantages in the markets, new products are created and improved with the corresponding development of technologies. In the analysis of previous publications, the role of the national innovation policy of the state in the system of forming priorities of investment activity in market conditions is noted. The purpose of the work is to study the features of building competition models of innovative processes. It should be emphasized that economic systems have a complex and heterogeneous structure with a hierarchical pattern of interaction of endogenous and exogenous factors. A common feature of many balance models of a market economy is the presence of autocatalytic components that determine the growth mechanisms of an innovative product. The article solves the problem of constructing and analyzing the behavioral properties of a mathematical model of competition between two economic entities in a common market. As a prototype for the model of endogenous homeodynamic system, the widely known mathematical model "predator-prey" is used in population dynamics. This model is a system of two ordinary differential equations with quadratic nonlinearities, which has several equilibrium positions and has a behavior with a change in the nature of stability. Research methods are based on the mathematical apparatus of economic synergetics and the theory of stability of nonlinear dynamic systems. As a result, the conditions under which the self-oscillating mode is implemented in the vicinity of the equilibrium state with the appearance of one or more limit cycles are specified. It has been established that the maximum number of limit cycles in the system under study around the equilibrium position is three. The subject analysis of the bifurcation properties of the cyclic dynamics of competitive interaction is carried out, the boundaries of stability loss by the equilibrium position are determined. Conclusions. The behavioral nature of the dynamics of innovation processes is changing significantly and it is possible to implement a leap transition from monotonous economic growth to relaxation fluctuations.