The paper proposes a method for mathematical modeling of socio-economic processes in organizational systems. The modeled processes include generating innovative knowledge and its transformation into a production technology that gives material profit. The mathematical model consists of four differential equations describing the dynamics of mutual conversion of such factors as employee motivation, dispersed tacit knowledge, corporate production information, and material product. The differential equations, which combine these factors, are based on the multifactor Cobb-Douglas production function. The author considers the mutual conversion of material and intangible factors of the production process from the perspective of the theory of intangible capital by P. Bourdieu, F. Fukuyama, and others. The numerical solution of the differential equation system using the Euler method allows identifying the features of the system phase diagrams depending on external influences, namely the intensity of the incoming information flow and the intensity of emotional costs. As a result of the bifurcation analysis of the phase diagrams, the values of the external influence parameters on the organizational system are established, at which the dynamics of knowledge generation and its transformation into production technology have the character of a “strange attractor”. The main practical recommendation is to manage the balance of the substitution elasticity indicators of material and intangible factors of production to maintain the stable state of the dynamic system under weakly predictable external influences.
A Tue, study studied this question.