Development of a stochastic model of innovative dynamics with a delay effect of interpersonal communications

The problem of controllability of complex socio-economic systems and the search for levers of influence that transfer them to the desired state remains relevant. This management is especially important in innovation systems - for example, in the framework of the release of innovative products and their introduction into the market, since innovation is currently the engine of the economy. The development process of such systems from the point of view of mathematics is considered as a dynamic model, and since when building dynamic systems, the effect of delay often occurs (for innovations, this is a delay in the process of consumer communication), this means that a delay in the response of the system for a certain period of time can be recorded. Therefore, when solving the problem of controllability of innovative processes, in particular, linear and nonlinear equations with a delay are used. Therefore, the purpose of the article is to develop and study an integral stochastic nonlinear model of the dynamics of indicators and processes to ensure sustainable development and forecasting in the framework of the development of an innovative economy.