Innovation dynamics of ecosystems and mathematical modeling of innovation diffusion

Abstract

The features of constructing mathematical models that are used to describe economic dynamics, and compares their mathematical apparatus and the scope of application of these models. The most complex, both for construction and for interpretation, is a mathematical model that takes into account the nonlinearity of economic development and the resulting synergistic effects. Using the example of a mathematical model of nonlinear dynamics proposed by the authors, the possibilities of using mathematical methods to study the diffusion of innovations and forecast the development of this process over time are demonstrated. With the help of this model, an analysis of the sustainability of innovation processes was carried out, critical parameters were determined, upon reaching which qualitative changes in the phase trajectories of the movement of the economic system are possible with its transition to a catastrophic mode, namely, the emergence of the Andronov-Hopf bifurcation and the birth of a limit cycle. An economic interpretation of the obtained results is given.