Complex dynamics of innovation diffusion

Abstract

In this study, the classical logistic model of the innovative product diffusion was considered. The development of the mathematical model was implemented on the basis of the dynamic balance of "demand - supply" in the innovation market both in discrete and continuous time. At the same time, the presence of a linear dependence of demand on the total volume of innovative products was taken into account, and on the supply side, the possibility of the existence of technological limitations of production was considered, which is reflected in the form of a quadratic dependence of the supply function on the number of innovative products. On the basis of the proposed mathematical model, simulation modeling was carried out, which illustrated such important dynamic modes as limit cycles with doubling of periods, irregular chaotic behavior and others.